%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:50:51 EDT 2023 % Result : Theorem 61.52s 9.35s % Output : Proof 238.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n008.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Fri Aug 25 13:33:47 EDT 2023 % 0.10/0.31 % CPUTime : % 0.15/0.59 ________ _____ % 0.15/0.59 ___ __ \_________(_)________________________________ % 0.15/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.59 % 0.15/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.59 (2023-06-19) % 0.15/0.59 % 0.15/0.59 (c) Philipp Rümmer, 2009-2023 % 0.15/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.59 Amanda Stjerna. % 0.15/0.59 Free software under BSD-3-Clause. % 0.15/0.59 % 0.15/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.59 % 0.15/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.61 Running up to 7 provers in parallel. % 0.15/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 14.56/2.74 Prover 0: Preprocessing ... % 14.56/2.75 Prover 4: Preprocessing ... % 14.56/2.80 Prover 1: Preprocessing ... % 15.22/2.84 Prover 2: Preprocessing ... % 15.74/2.88 Prover 6: Preprocessing ... % 15.74/2.95 Prover 3: Preprocessing ... % 16.36/2.98 Prover 5: Preprocessing ... % 54.16/8.16 Prover 3: Warning: ignoring some quantifiers % 55.05/8.27 Prover 3: Constructing countermodel ... % 55.72/8.33 Prover 1: Warning: ignoring some quantifiers % 55.88/8.45 Prover 6: Proving ... % 55.88/8.60 Prover 1: Constructing countermodel ... % 61.52/9.34 Prover 3: proved (8721ms) % 61.52/9.34 % 61.52/9.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 61.52/9.35 % 61.52/9.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 61.52/9.35 Prover 6: stopped % 61.52/9.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 62.13/9.40 Prover 4: Warning: ignoring some quantifiers % 62.13/9.41 Prover 0: Proving ... % 62.13/9.41 Prover 0: stopped % 62.13/9.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 65.30/9.70 Prover 4: Constructing countermodel ... % 67.34/10.04 Prover 8: Preprocessing ... % 70.46/10.36 Prover 10: Preprocessing ... % 71.02/10.44 Prover 7: Preprocessing ... % 74.04/11.05 Prover 5: Proving ... % 74.04/11.05 Prover 5: stopped % 74.04/11.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 83.23/12.04 Prover 11: Preprocessing ... % 84.32/12.18 Prover 8: Warning: ignoring some quantifiers % 84.66/12.23 Prover 10: Warning: ignoring some quantifiers % 85.59/12.36 Prover 10: Constructing countermodel ... % 85.93/12.38 Prover 8: Constructing countermodel ... % 91.22/13.20 Prover 2: Proving ... % 91.22/13.20 Prover 2: stopped % 91.22/13.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 94.23/13.50 Prover 7: Warning: ignoring some quantifiers % 96.49/13.79 Prover 7: Constructing countermodel ... % 96.65/13.99 Prover 13: Preprocessing ... % 105.98/15.11 Prover 11: Warning: ignoring some quantifiers % 107.39/15.35 Prover 11: Constructing countermodel ... % 112.22/15.96 Prover 1: stopped % 112.22/15.96 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 119.81/17.03 Prover 16: Preprocessing ... % 120.34/17.28 Prover 13: Warning: ignoring some quantifiers % 124.32/17.60 Prover 13: Constructing countermodel ... % 132.22/18.68 Prover 16: Warning: ignoring some quantifiers % 132.22/18.82 Prover 16: Constructing countermodel ... % 148.49/20.83 Prover 16: stopped % 148.49/20.86 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 152.57/21.51 Prover 19: Preprocessing ... % 159.96/22.38 Prover 13: stopped % 170.83/24.05 Prover 19: Warning: ignoring some quantifiers % 174.00/24.22 Prover 19: Constructing countermodel ... % 202.05/27.91 Prover 19: stopped % 202.05/27.95 Prover 4: stopped % 213.49/29.70 Prover 7: stopped % 232.10/34.57 Prover 8: Found proof (size 1383) % 232.10/34.57 Prover 8: proved (25048ms) % 232.10/34.57 Prover 10: stopped % 232.10/34.58 Prover 11: stopped % 232.10/34.58 % 232.10/34.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 232.10/34.58 % 235.84/36.67 % SZS output start Proof for theBenchmark % 235.84/36.69 Assumptions after simplification: % 235.84/36.69 --------------------------------- % 235.84/36.69 % 235.84/36.69 (conj_0) % 235.84/36.72 $i(pls) & $i(n) & $i(semiri1621563631at_int) & $i(one_one_int) & % 235.84/36.72 $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 235.84/36.72 [v4: $i] : ? [v5: $i] : ? [v6: $i] : (bit1(pls) = v4 & bit0(v4) = v5 & % 235.84/36.72 number_number_of_nat(v5) = v6 & power_power_int(v2) = v3 & % 235.84/36.72 plus_plus_int(one_one_int) = v0 & hAPP_nat_int(v3, v6) = zero_zero_int & % 235.84/36.72 hAPP_nat_int(semiri1621563631at_int, n) = v1 & hAPP_int_int(v0, v1) = v2 & % 235.84/36.72 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 235.84/36.72 % 235.84/36.72 (fact_0_n1pos) % 235.84/36.72 $i(n) & $i(semiri1621563631at_int) & $i(one_one_int) & $i(zero_zero_int) & % 235.84/36.72 $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 235.84/36.72 [v4: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & % 235.84/36.72 plus_plus_int(one_one_int) = v1 & hAPP_nat_int(semiri1621563631at_int, n) = % 235.84/36.72 v2 & hAPP_int_int(v1, v2) = v3 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 % 235.84/36.72 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 235.84/36.72 % 235.84/36.72 (fact_106_semiring__numeral__0__eq__0) % 235.84/36.72 number_number_of_int(pls) = zero_zero_int & $i(pls) & $i(zero_zero_int) % 235.84/36.72 % 235.84/36.72 (fact_109_number__of__Pls) % 235.84/36.72 number_number_of_int(pls) = zero_zero_int & $i(pls) & $i(zero_zero_int) % 235.84/36.72 % 235.84/36.72 (fact_10_zero__eq__power2) % 235.84/36.72 $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 235.84/36.72 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 235.84/36.72 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v3 = zero_zero_int | ~ % 235.84/36.72 (power_power_int(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = % 235.84/36.72 zero_zero_int) & hAPP_nat_int(v4, v2) = v5 & $i(v5))) & ! [v3: $i] : % 235.84/36.72 ( ~ (power_power_int(zero_zero_int) = v3) | hAPP_nat_int(v3, v2) = % 235.84/36.72 zero_zero_int)) % 235.84/36.72 % 235.84/36.72 (fact_111_semiring__norm_I112_J) % 235.84/36.72 number_number_of_int(pls) = zero_zero_int & $i(pls) & $i(zero_zero_int) % 235.84/36.72 % 235.84/36.72 (fact_113_add__numeral__0) % 235.84/36.73 $i(pls) & ? [v0: $i] : ? [v1: $i] : (number_number_of_int(pls) = v0 & % 235.84/36.73 plus_plus_int(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = % 235.84/36.73 v2 | ~ (hAPP_int_int(v1, v2) = v3) | ~ $i(v2))) % 235.84/36.73 % 235.84/36.73 (fact_115_add__numeral__0__right) % 235.84/36.73 $i(pls) & ? [v0: $i] : (number_number_of_int(pls) = v0 & $i(v0) & ! [v1: $i] % 235.84/36.73 : ! [v2: $i] : ( ~ (plus_plus_int(v1) = v2) | ~ $i(v1) | hAPP_int_int(v2, % 235.84/36.73 v0) = v1)) % 235.84/36.73 % 235.84/36.73 (fact_117_power__eq__0__iff__number__of) % 235.84/36.73 $i(zero_zero_nat) & $i(zero_zero_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 235.84/36.73 $i] : ! [v3: $i] : (v3 = zero_zero_int | v1 = zero_zero_nat | ~ % 235.84/36.73 (number_number_of_nat(v0) = v1) | ~ (power_power_int(zero_zero_int) = v2) | % 235.84/36.73 ~ (hAPP_nat_int(v2, v1) = v3) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 235.84/36.73 [v2: $i] : ! [v3: $i] : ( ~ (number_number_of_nat(v1) = v3) | ~ % 235.84/36.73 (power_power_int(v0) = v2) | ~ (hAPP_nat_int(v2, v3) = zero_zero_int) | ~ % 235.84/36.73 $i(v1) | ~ $i(v0) | (v0 = zero_zero_int & ~ (v3 = zero_zero_nat))) % 235.84/36.73 % 235.84/36.73 (fact_11_zero__eq__power2) % 235.84/36.73 $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 235.84/36.73 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 235.84/36.73 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v3 = zero_zero_real | ~ % 235.84/36.73 (power_power_real(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = % 235.84/36.73 zero_zero_real) & hAPP_nat_real(v4, v2) = v5 & $i(v5))) & ! [v3: $i] % 235.84/36.73 : ( ~ (power_power_real(zero_zero_real) = v3) | hAPP_nat_real(v3, v2) = % 235.84/36.73 zero_zero_real)) % 235.84/36.73 % 235.84/36.73 (fact_128_Bit1__def) % 235.84/36.73 $i(one_one_int) & ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! % 235.84/36.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) % 235.84/36.73 = v3) | ~ (hAPP_int_int(v3, v1) = v4) | ~ (hAPP_int_int(v0, v1) = v2) % 235.84/36.73 | ~ $i(v1) | (bit1(v1) = v4 & $i(v4)))) % 235.84/36.73 % 235.84/36.73 (fact_129_odd__nonzero) % 235.84/36.74 $i(one_one_int) & $i(zero_zero_int) & ? [v0: $i] : % 235.84/36.74 (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 235.84/36.74 [v3: $i] : ( ~ (plus_plus_int(v2) = v3) | ~ (hAPP_int_int(v3, v1) = % 235.84/36.74 zero_zero_int) | ~ (hAPP_int_int(v0, v1) = v2) | ~ $i(v1))) % 235.84/36.74 % 235.84/36.74 (fact_12_add__special_I2_J) % 235.84/36.74 $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 235.84/36.74 (bit1(pls) = v1 & plus_plus_int(v1) = v2 & plus_plus_int(one_one_int) = v0 & % 235.84/36.74 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_int(v2, % 235.84/36.74 v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 235.84/36.74 (number_number_of_int(v4) = v6 & number_number_of_int(v3) = v5 & % 235.84/36.74 hAPP_int_int(v0, v5) = v6 & $i(v6) & $i(v5)))) % 235.84/36.74 % 235.84/36.74 (fact_131_number__of__int) % 235.84/36.74 $i(semiri1621563631at_int) & ! [v0: $i] : ! [v1: $i] : ( ~ % 235.84/36.74 (hAPP_nat_int(semiri1621563631at_int, v0) = v1) | ~ $i(v0) | % 235.84/36.74 (number_number_of_int(v1) = v1 & $i(v1))) % 235.84/36.74 % 235.84/36.74 (fact_133_zero__less__power2) % 235.84/36.74 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.74 ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 & bit0(v1) = v2 & % 235.84/36.74 number_number_of_nat(v2) = v3 & hAPP_i1948725293t_bool(ord_less_int, % 235.84/36.74 zero_zero_int) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 235.84/36.74 [v5: $i] : (v4 = zero_zero_int | ~ (power_power_int(v4) = v5) | ~ $i(v4) | % 235.84/36.74 ? [v6: $i] : ? [v7: $i] : (hAPP_nat_int(v5, v3) = v6 & hBOOL(v7) = 0 & % 235.84/36.74 hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6))) & ! [v4: $i] : ( ~ % 235.84/36.74 (power_power_int(zero_zero_int) = v4) | ? [v5: $i] : ? [v6: $i] : ? % 235.84/36.74 [v7: int] : ( ~ (v7 = 0) & hAPP_nat_int(v4, v3) = v5 & hBOOL(v6) = v7 & % 235.84/36.74 hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5)))) % 235.84/36.74 % 235.84/36.74 (fact_134_zero__less__power2) % 235.84/36.75 $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.75 ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_real, % 235.84/36.75 zero_zero_real) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 235.84/36.75 number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 235.84/36.75 $i] : ! [v5: $i] : (v4 = zero_zero_real | ~ (power_power_real(v4) = v5) % 235.84/36.75 | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] : (hAPP_nat_real(v5, v3) = v6 & % 235.84/36.75 hBOOL(v7) = 0 & hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6))) & ! % 235.84/36.75 [v4: $i] : ( ~ (power_power_real(zero_zero_real) = v4) | ? [v5: $i] : ? % 235.84/36.75 [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & hAPP_nat_real(v4, v3) = v5 & % 235.84/36.75 hBOOL(v6) = v7 & hAPP_real_bool(v0, v5) = v6 & $i(v6) & $i(v5)))) % 235.84/36.75 % 235.84/36.75 (fact_135_power2__less__0) % 235.84/36.75 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.75 ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 235.84/36.75 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 235.84/36.75 (power_power_int(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? % 235.84/36.75 [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 235.84/36.75 hAPP_i1948725293t_bool(ord_less_int, v5) = v6 & hAPP_nat_int(v4, v2) = % 235.84/36.75 v5 & hBOOL(v7) = v8 & hAPP_int_bool(v6, zero_zero_int) = v7 & $i(v7) & % 235.84/36.75 $i(v6) & $i(v5)))) % 235.84/36.75 % 235.84/36.75 (fact_136_power2__less__0) % 235.84/36.75 $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.75 ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 % 235.84/36.75 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 235.84/36.75 (power_power_real(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? % 235.84/36.75 [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 235.84/36.75 hAPP_r1134773055l_bool(ord_less_real, v5) = v6 & hAPP_nat_real(v4, v2) = % 235.84/36.75 v5 & hBOOL(v7) = v8 & hAPP_real_bool(v6, zero_zero_real) = v7 & $i(v7) & % 235.84/36.75 $i(v6) & $i(v5)))) % 235.84/36.75 % 235.84/36.75 (fact_137_sum__power2__gt__zero__iff) % 235.84/36.75 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.75 ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 & bit0(v1) = v2 & % 235.84/36.75 number_number_of_nat(v2) = v3 & hAPP_i1948725293t_bool(ord_less_int, % 235.84/36.75 zero_zero_int) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 235.84/36.75 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 235.84/36.75 $i] : ! [v11: $i] : ( ~ (power_power_int(v5) = v9) | ~ % 235.84/36.75 (power_power_int(v4) = v6) | ~ (plus_plus_int(v7) = v8) | ~ % 235.84/36.75 (hAPP_nat_int(v9, v3) = v10) | ~ (hAPP_nat_int(v6, v3) = v7) | ~ % 235.84/36.75 (hAPP_int_int(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 235.84/36.75 (hBOOL(v12) = 0 & hAPP_int_bool(v0, v11) = v12 & $i(v12)) | (v5 = % 235.84/36.75 zero_zero_int & v4 = zero_zero_int)) & ! [v4: $i] : ! [v5: $i] : ! % 235.84/36.75 [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(zero_zero_int) = v4) | ~ % 235.84/36.75 (plus_plus_int(v5) = v6) | ~ (hAPP_nat_int(v4, v3) = v5) | ~ % 235.84/36.75 (hAPP_int_int(v6, v5) = v7) | ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & % 235.84/36.75 hBOOL(v8) = v9 & hAPP_int_bool(v0, v7) = v8 & $i(v8)))) % 235.84/36.75 % 235.84/36.75 (fact_138_sum__power2__gt__zero__iff) % 235.84/36.76 $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.76 ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_real, % 235.84/36.76 zero_zero_real) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 235.84/36.76 number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 235.84/36.76 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 235.84/36.76 : ! [v10: $i] : ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 235.84/36.76 (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 235.84/36.76 (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | ~ % 235.84/36.76 (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 235.84/36.76 (hBOOL(v12) = 0 & hAPP_real_bool(v0, v11) = v12 & $i(v12)) | (v5 = % 235.84/36.76 zero_zero_real & v4 = zero_zero_real)) & ! [v4: $i] : ! [v5: $i] : ! % 235.84/36.76 [v6: $i] : ! [v7: $i] : ( ~ (plus_plus_real(v5) = v6) | ~ % 235.84/36.76 (power_power_real(zero_zero_real) = v4) | ~ (hAPP_nat_real(v4, v3) = v5) % 235.84/36.76 | ~ (hAPP_real_real(v6, v5) = v7) | ? [v8: $i] : ? [v9: int] : ( ~ (v9 % 235.84/36.76 = 0) & hBOOL(v8) = v9 & hAPP_real_bool(v0, v7) = v8 & $i(v8)))) % 235.84/36.76 % 235.84/36.76 (fact_139_not__sum__power2__lt__zero) % 235.84/36.76 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 235.84/36.76 ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 235.84/36.76 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 235.84/36.76 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 235.84/36.76 (power_power_int(v4) = v8) | ~ (power_power_int(v3) = v5) | ~ % 235.84/36.76 (plus_plus_int(v6) = v7) | ~ (hAPP_nat_int(v8, v2) = v9) | ~ % 235.84/36.76 (hAPP_nat_int(v5, v2) = v6) | ~ (hAPP_int_int(v7, v9) = v10) | ~ $i(v4) % 235.84/36.76 | ~ $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: int] : ( ~ (v13 = 0) % 235.84/36.76 & hAPP_i1948725293t_bool(ord_less_int, v10) = v11 & hBOOL(v12) = v13 & % 235.84/36.76 hAPP_int_bool(v11, zero_zero_int) = v12 & $i(v12) & $i(v11)))) % 235.84/36.76 % 235.84/36.76 (fact_13_add__special_I2_J) % 236.39/36.76 $i(one_one_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.39/36.76 (plus_plus_real(one_one_real) = v0 & bit1(pls) = v1 & plus_plus_int(v1) = v2 & % 236.39/36.76 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_int(v2, % 236.39/36.76 v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 236.39/36.76 (number267125858f_real(v4) = v6 & number267125858f_real(v3) = v5 & % 236.39/36.76 hAPP_real_real(v0, v5) = v6 & $i(v6) & $i(v5)))) % 236.39/36.76 % 236.39/36.76 (fact_140_not__sum__power2__lt__zero) % 236.39/36.76 $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.76 ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 % 236.39/36.76 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 236.39/36.76 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 236.39/36.76 (plus_plus_real(v6) = v7) | ~ (power_power_real(v4) = v8) | ~ % 236.39/36.76 (power_power_real(v3) = v5) | ~ (hAPP_nat_real(v8, v2) = v9) | ~ % 236.39/36.76 (hAPP_nat_real(v5, v2) = v6) | ~ (hAPP_real_real(v7, v9) = v10) | ~ % 236.39/36.76 $i(v4) | ~ $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: int] : ( ~ % 236.39/36.76 (v13 = 0) & hAPP_r1134773055l_bool(ord_less_real, v10) = v11 & % 236.39/36.76 hBOOL(v12) = v13 & hAPP_real_bool(v11, zero_zero_real) = v12 & $i(v12) & % 236.39/36.76 $i(v11)))) % 236.39/36.76 % 236.39/36.76 (fact_143_number__of__Bit1) % 236.39/36.77 $i(one_one_int) & ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! % 236.39/36.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 236.39/36.77 (number_number_of_int(v1) = v2) | ~ (plus_plus_int(v3) = v4) | ~ % 236.39/36.77 (hAPP_int_int(v4, v2) = v5) | ~ (hAPP_int_int(v0, v2) = v3) | ~ $i(v1) | % 236.39/36.77 ? [v6: $i] : (number_number_of_int(v6) = v5 & bit1(v1) = v6 & $i(v6) & % 236.39/36.77 $i(v5)))) % 236.39/36.77 % 236.39/36.77 (fact_145_semiring__numeral__1__eq__1) % 236.39/36.77 $i(pls) & $i(one_one_int) & ? [v0: $i] : (number_number_of_int(v0) = % 236.39/36.77 one_one_int & bit1(pls) = v0 & $i(v0)) % 236.39/36.77 % 236.39/36.77 (fact_146_semiring__numeral__1__eq__1) % 236.39/36.77 $i(one_one_nat) & $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & % 236.39/36.77 number_number_of_nat(v0) = one_one_nat & $i(v0)) % 236.39/36.77 % 236.39/36.77 (fact_147_semiring__numeral__1__eq__1) % 236.39/36.77 $i(one_one_real) & $i(pls) & ? [v0: $i] : (number267125858f_real(v0) = % 236.39/36.77 one_one_real & bit1(pls) = v0 & $i(v0)) % 236.39/36.77 % 236.39/36.77 (fact_148_mn) % 236.39/36.77 $i(m1) & $i(n) & $i(semiri1621563631at_int) & $i(one_one_int) & % 236.39/36.77 $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 236.39/36.77 [v4: $i] : (hAPP_i1948725293t_bool(ord_less_int, m1) = v0 & % 236.39/36.77 plus_plus_int(one_one_int) = v1 & hAPP_nat_int(semiri1621563631at_int, n) = % 236.39/36.77 v2 & hAPP_int_int(v1, v2) = v3 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 % 236.39/36.77 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.77 % 236.39/36.77 (fact_149_of__nat__less__two__power) % 236.39/36.77 $i(pls) & $i(semiri1621563631at_int) & $i(ord_less_int) & ? [v0: $i] : ? % 236.39/36.77 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (number_number_of_int(v1) = v2 & % 236.39/36.77 bit1(pls) = v0 & bit0(v0) = v1 & power_power_int(v2) = v3 & $i(v3) & $i(v2) % 236.39/36.77 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 236.39/36.77 ! [v8: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~ % 236.39/36.77 (hAPP_nat_int(v3, v4) = v7) | ~ (hAPP_nat_int(semiri1621563631at_int, v4) % 236.39/36.77 = v5) | ~ (hAPP_int_bool(v6, v7) = v8) | ~ $i(v4) | hBOOL(v8) = 0)) % 236.39/36.77 % 236.39/36.77 (fact_14_add__special_I3_J) % 236.39/36.77 $i(pls) & $i(one_one_int) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: % 236.39/36.77 $i] : ! [v2: $i] : ( ~ (number_number_of_int(v1) = v2) | ~ $i(v1) | ? % 236.39/36.77 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 236.39/36.77 (number_number_of_int(v6) = v4 & plus_plus_int(v2) = v3 & % 236.39/36.77 plus_plus_int(v1) = v5 & hAPP_int_int(v5, v0) = v6 & hAPP_int_int(v3, % 236.39/36.77 one_one_int) = v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3)))) % 236.39/36.77 % 236.39/36.77 (fact_150_of__nat__less__two__power) % 236.39/36.77 $i(semiri132038758t_real) & $i(ord_less_real) & $i(pls) & ? [v0: $i] : ? % 236.39/36.77 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (number267125858f_real(v1) = v2 & % 236.39/36.77 power_power_real(v2) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & $i(v3) & $i(v2) % 236.39/36.77 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 236.39/36.77 ! [v8: $i] : ( ~ (hAPP_r1134773055l_bool(ord_less_real, v5) = v6) | ~ % 236.39/36.77 (hAPP_nat_real(v3, v4) = v7) | ~ (hAPP_nat_real(semiri132038758t_real, % 236.39/36.77 v4) = v5) | ~ (hAPP_real_bool(v6, v7) = v8) | ~ $i(v4) | hBOOL(v8) = % 236.39/36.77 0)) % 236.39/36.77 % 236.39/36.77 (fact_151_transfer__int__nat__numerals_I3_J) % 236.39/36.77 $i(pls) & $i(semiri1621563631at_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 236.39/36.77 : ? [v3: $i] : (number_number_of_int(v1) = v2 & bit1(pls) = v0 & bit0(v0) = % 236.39/36.77 v1 & number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int, % 236.39/36.77 v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.77 % 236.39/36.77 (fact_152_transfer__int__nat__numerals_I4_J) % 236.39/36.78 $i(pls) & $i(semiri1621563631at_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 236.39/36.78 : ? [v3: $i] : (number_number_of_int(v1) = v2 & bit1(v0) = v1 & bit1(pls) = % 236.39/36.78 v0 & number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int, % 236.39/36.78 v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.78 % 236.39/36.78 (fact_153_realpow__two__sum__zero__iff) % 236.39/36.78 $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.39/36.78 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 236.39/36.78 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 236.39/36.78 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (plus_plus_real(v6) = v7) | ~ % 236.39/36.78 (power_power_real(v4) = v8) | ~ (power_power_real(v3) = v5) | ~ % 236.39/36.78 (hAPP_nat_real(v8, v2) = v9) | ~ (hAPP_nat_real(v5, v2) = v6) | ~ % 236.39/36.78 (hAPP_real_real(v7, v9) = zero_zero_real) | ~ $i(v4) | ~ $i(v3) | (v4 = % 236.39/36.78 zero_zero_real & v3 = zero_zero_real)) & ! [v3: $i] : ! [v4: $i] : ! % 236.39/36.78 [v5: $i] : ! [v6: $i] : (v6 = zero_zero_real | ~ (plus_plus_real(v4) = v5) % 236.39/36.78 | ~ (power_power_real(zero_zero_real) = v3) | ~ (hAPP_nat_real(v3, v2) = % 236.39/36.78 v4) | ~ (hAPP_real_real(v5, v4) = v6))) % 236.39/36.78 % 236.39/36.78 (fact_154_of__nat__0__less__iff) % 236.39/36.78 $i(ord_less_nat) & $i(zero_zero_nat) & $i(semiri1621563631at_int) & % 236.39/36.78 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.78 (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v1 & % 236.39/36.78 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v1) & $i(v0) & % 236.39/36.78 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | % 236.39/36.78 ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.39/36.78 (hAPP_nat_int(semiri1621563631at_int, v2) = v5 & hBOOL(v6) = v7 & % 236.39/36.78 hBOOL(v3) = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 % 236.39/36.78 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 236.39/36.78 (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? % 236.39/36.78 [v6: any] : ? [v7: any] : (hAPP_nat_int(semiri1621563631at_int, v2) = v4 % 236.39/36.78 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) % 236.39/36.78 & $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 236.39/36.78 % 236.39/36.78 (fact_15_add__special_I3_J) % 236.39/36.78 $i(one_one_real) & $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: % 236.39/36.78 $i] : ! [v2: $i] : ( ~ (number267125858f_real(v1) = v2) | ~ $i(v1) | ? % 236.39/36.78 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 236.39/36.78 (number267125858f_real(v6) = v4 & plus_plus_real(v2) = v3 & % 236.39/36.78 hAPP_real_real(v3, one_one_real) = v4 & plus_plus_int(v1) = v5 & % 236.39/36.78 hAPP_int_int(v5, v0) = v6 & $i(v6) & $i(v5) & $i(v4) & $i(v3)))) % 236.39/36.78 % 236.39/36.78 (fact_163_power__strict__decreasing) % 236.39/36.78 $i(ord_less_nat) & $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & ? % 236.39/36.78 [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) % 236.39/36.78 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 236.39/36.78 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (power_power_int(v1) = v4) | ~ % 236.39/36.78 (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~ (hAPP_nat_int(v4, v3) % 236.39/36.78 = v5) | ~ (hAPP_nat_int(v4, v2) = v7) | ~ (hAPP_int_bool(v6, v7) = v8) % 236.39/36.78 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v9: $i] : ? [v10: $i] : ? % 236.39/36.78 [v11: any] : ? [v12: $i] : ? [v13: any] : ? [v14: $i] : ? [v15: $i] : % 236.39/36.78 ? [v16: any] : ? [v17: any] : (hAPP_n1699378549t_bool(ord_less_nat, v2) = % 236.39/36.78 v9 & hAPP_i1948725293t_bool(ord_less_int, v1) = v14 & hBOOL(v15) = v16 & % 236.39/36.78 hBOOL(v12) = v13 & hBOOL(v10) = v11 & hBOOL(v8) = v17 & % 236.39/36.78 hAPP_nat_bool(v9, v3) = v10 & hAPP_int_bool(v14, one_one_int) = v15 & % 236.39/36.78 hAPP_int_bool(v0, v1) = v12 & $i(v15) & $i(v14) & $i(v12) & $i(v10) & % 236.39/36.78 $i(v9) & ( ~ (v16 = 0) | ~ (v13 = 0) | ~ (v11 = 0) | v17 = 0)))) % 236.39/36.78 % 236.39/36.79 (fact_166_zero__less__two) % 236.39/36.79 $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: % 236.39/36.79 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_i1948725293t_bool(ord_less_int, % 236.39/36.79 zero_zero_int) = v0 & plus_plus_int(one_one_int) = v1 & hAPP_int_int(v1, % 236.39/36.79 one_one_int) = v2 & hBOOL(v3) = 0 & hAPP_int_bool(v0, v2) = v3 & $i(v3) & % 236.39/36.79 $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_167_zero__less__two) % 236.39/36.79 $i(ord_less_nat) & $i(zero_zero_nat) & $i(one_one_nat) & ? [v0: $i] : ? [v1: % 236.39/36.79 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_n1699378549t_bool(ord_less_nat, % 236.39/36.79 zero_zero_nat) = v0 & plus_plus_nat(one_one_nat) = v1 & hAPP_nat_nat(v1, % 236.39/36.79 one_one_nat) = v2 & hBOOL(v3) = 0 & hAPP_nat_bool(v0, v2) = v3 & $i(v3) & % 236.39/36.79 $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_16_one__add__one__is__two) % 236.39/36.79 $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.79 $i] : (number_number_of_int(v3) = v1 & bit1(pls) = v2 & bit0(v2) = v3 & % 236.39/36.79 plus_plus_int(one_one_int) = v0 & hAPP_int_int(v0, one_one_int) = v1 & % 236.39/36.79 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_17_one__add__one__is__two) % 236.39/36.79 $i(one_one_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.79 $i] : (number267125858f_real(v3) = v1 & plus_plus_real(one_one_real) = v0 & % 236.39/36.79 hAPP_real_real(v0, one_one_real) = v1 & bit1(pls) = v2 & bit0(v2) = v3 & % 236.39/36.79 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_18_semiring__one__add__one__is__two) % 236.39/36.79 $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.79 $i] : (number_number_of_int(v3) = v1 & bit1(pls) = v2 & bit0(v2) = v3 & % 236.39/36.79 plus_plus_int(one_one_int) = v0 & hAPP_int_int(v0, one_one_int) = v1 & % 236.39/36.79 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_19_semiring__one__add__one__is__two) % 236.39/36.79 $i(one_one_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.79 $i] : (plus_plus_nat(one_one_nat) = v0 & hAPP_nat_nat(v0, one_one_nat) = v1 % 236.39/36.79 & bit1(pls) = v2 & bit0(v2) = v3 & number_number_of_nat(v3) = v1 & $i(v3) & % 236.39/36.79 $i(v2) & $i(v1) & $i(v0)) % 236.39/36.79 % 236.39/36.79 (fact_207_less__nat__number__of) % 236.39/36.79 $i(ord_less_nat) & $i(pls) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.79 (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & $i(v0) & ! [v1: $i] : ! % 236.39/36.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 236.39/36.79 (hAPP_n1699378549t_bool(ord_less_nat, v3) = v4) | ~ % 236.39/36.79 (number_number_of_nat(v2) = v5) | ~ (number_number_of_nat(v1) = v3) | ~ % 236.39/36.79 (hAPP_nat_bool(v4, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ? [v7: any] : ? % 236.39/36.79 [v8: $i] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: any] : % 236.39/36.79 (hAPP_i1948725293t_bool(ord_less_int, v1) = v8 & hBOOL(v11) = v12 & % 236.39/36.79 hBOOL(v9) = v10 & hBOOL(v6) = v7 & hAPP_int_bool(v8, v2) = v9 & % 236.39/36.79 hAPP_int_bool(v0, v2) = v11 & $i(v11) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | % 236.39/36.79 (v12 = 0 & v10 = 0)))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 236.39/36.79 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 236.39/36.79 (hAPP_n1699378549t_bool(ord_less_nat, v3) = v4) | ~ % 236.39/36.79 (number_number_of_nat(v2) = v5) | ~ (number_number_of_nat(v1) = v3) | ~ % 236.39/36.79 (hAPP_nat_bool(v4, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ? [v7: $i] : ? % 236.39/36.79 [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 236.39/36.79 (hAPP_i1948725293t_bool(ord_less_int, v1) = v7 & hBOOL(v10) = v11 & % 236.39/36.79 hBOOL(v8) = v9 & hBOOL(v6) = v12 & hAPP_int_bool(v7, v2) = v8 & % 236.39/36.79 hAPP_int_bool(v0, v2) = v10 & $i(v10) & $i(v8) & $i(v7) & ( ~ (v11 = 0) % 236.39/36.79 | ~ (v9 = 0) | v12 = 0)))) % 236.39/36.79 % 236.39/36.79 (fact_20_semiring__one__add__one__is__two) % 236.39/36.80 $i(one_one_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.80 $i] : (number267125858f_real(v3) = v1 & plus_plus_real(one_one_real) = v0 & % 236.39/36.80 hAPP_real_real(v0, one_one_real) = v1 & bit1(pls) = v2 & bit0(v2) = v3 & % 236.39/36.80 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.80 % 236.39/36.80 (fact_21_quartic__square__square) % 236.39/36.80 $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 236.39/36.80 : (bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) = v1 & number_number_of_nat(v3) = % 236.39/36.80 v4 & number_number_of_nat(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 236.39/36.80 $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~ (power_power_int(v5) = v6) | ~ % 236.39/36.80 $i(v5) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (power_power_int(v7) = % 236.39/36.80 v8 & hAPP_nat_int(v8, v2) = v9 & hAPP_nat_int(v6, v4) = v9 & % 236.39/36.80 hAPP_nat_int(v6, v2) = v7 & $i(v9) & $i(v8) & $i(v7)))) % 236.39/36.80 % 236.39/36.80 (fact_222_less__0__number__of) % 236.39/36.80 $i(ord_less_nat) & $i(zero_zero_nat) & $i(pls) & $i(ord_less_int) & ? [v0: % 236.39/36.80 $i] : ? [v1: $i] : (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = % 236.39/36.80 v0 & hAPP_i1948725293t_bool(ord_less_int, pls) = v1 & $i(v1) & $i(v0) & ! % 236.39/36.80 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? % 236.39/36.80 [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.39/36.80 (number_number_of_nat(v2) = v5 & hBOOL(v6) = v7 & hBOOL(v3) = v4 & % 236.39/36.80 hAPP_nat_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = 0))) % 236.39/36.80 & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | % 236.39/36.80 ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 236.39/36.80 (number_number_of_nat(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & % 236.39/36.80 hAPP_nat_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 236.39/36.80 % 236.39/36.80 (fact_223_zero__less__int__conv) % 236.39/36.80 $i(ord_less_nat) & $i(zero_zero_nat) & $i(semiri1621563631at_int) & % 236.39/36.80 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.80 (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v1 & % 236.39/36.80 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v1) & $i(v0) & % 236.39/36.80 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | % 236.39/36.80 ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.39/36.80 (hAPP_nat_int(semiri1621563631at_int, v2) = v5 & hBOOL(v6) = v7 & % 236.39/36.80 hBOOL(v3) = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 % 236.39/36.80 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 236.39/36.80 (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? % 236.39/36.80 [v6: any] : ? [v7: any] : (hAPP_nat_int(semiri1621563631at_int, v2) = v4 % 236.39/36.80 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) % 236.39/36.80 & $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 236.39/36.80 % 236.39/36.80 (fact_249_of__nat__1) % 236.39/36.80 hAPP_nat_int(semiri1621563631at_int, one_one_nat) = one_one_int & % 236.39/36.80 $i(one_one_nat) & $i(semiri1621563631at_int) & $i(one_one_int) % 236.39/36.80 % 236.39/36.80 (fact_253_transfer__int__nat__numerals_I2_J) % 236.39/36.80 hAPP_nat_int(semiri1621563631at_int, one_one_nat) = one_one_int & % 236.39/36.80 $i(one_one_nat) & $i(semiri1621563631at_int) & $i(one_one_int) % 236.39/36.80 % 236.39/36.80 (fact_258_pos__add__strict) % 236.39/36.81 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.81 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1: % 236.39/36.81 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 236.39/36.81 : ! [v7: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ % 236.39/36.81 (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 236.39/36.81 (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: % 236.39/36.81 $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 236.39/36.81 (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v7) = v12 & hAPP_int_bool(v4, % 236.39/36.81 v2) = v10 & hAPP_int_bool(v0, v3) = v8 & $i(v10) & $i(v8) & ( ~ (v11 = % 236.39/36.81 0) | ~ (v9 = 0) | v12 = 0)))) % 236.39/36.81 % 236.39/36.81 (fact_25_semiring__norm_I110_J) % 236.39/36.81 $i(pls) & $i(one_one_int) & ? [v0: $i] : (number_number_of_int(v0) = % 236.39/36.81 one_one_int & bit1(pls) = v0 & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_264_zero__less__one) % 236.39/36.81 $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: % 236.39/36.81 $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & hBOOL(v1) % 236.39/36.81 = 0 & hAPP_int_bool(v0, one_one_int) = v1 & $i(v1) & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_267_zero__less__power) % 236.39/36.81 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.81 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1: % 236.39/36.81 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (power_power_int(v2) = % 236.39/36.81 v3) | ~ (hAPP_nat_int(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: % 236.39/36.81 $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8 & % 236.39/36.81 hBOOL(v5) = v6 & hAPP_int_bool(v0, v4) = v7 & hAPP_int_bool(v0, v2) = v5 % 236.39/36.81 & $i(v7) & $i(v5) & ( ~ (v6 = 0) | v8 = 0)))) % 236.39/36.81 % 236.39/36.81 (fact_26_semiring__norm_I110_J) % 236.39/36.81 $i(one_one_real) & $i(pls) & ? [v0: $i] : (number267125858f_real(v0) = % 236.39/36.81 one_one_real & bit1(pls) = v0 & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_27_numeral__1__eq__1) % 236.39/36.81 $i(pls) & $i(one_one_int) & ? [v0: $i] : (number_number_of_int(v0) = % 236.39/36.81 one_one_int & bit1(pls) = v0 & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_28_numeral__1__eq__1) % 236.39/36.81 $i(one_one_real) & $i(pls) & ? [v0: $i] : (number267125858f_real(v0) = % 236.39/36.81 one_one_real & bit1(pls) = v0 & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_296_pos2) % 236.39/36.81 $i(ord_less_nat) & $i(zero_zero_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.81 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (hAPP_n1699378549t_bool(ord_less_nat, % 236.39/36.81 zero_zero_nat) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 236.39/36.81 number_number_of_nat(v2) = v3 & hBOOL(v4) = 0 & hAPP_nat_bool(v0, v3) = v4 & % 236.39/36.81 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.39/36.81 % 236.39/36.81 (fact_297_zero__less__imp__eq__int) % 236.39/36.81 $i(ord_less_nat) & $i(zero_zero_nat) & $i(semiri1621563631at_int) & % 236.39/36.81 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.81 (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v1 & % 236.39/36.81 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v1) & $i(v0) & % 236.39/36.81 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | % 236.39/36.81 ? [v4: $i] : ? [v5: $i] : (hAPP_nat_int(semiri1621563631at_int, v4) = v2 % 236.39/36.81 & hBOOL(v5) = 0 & hAPP_nat_bool(v1, v4) = v5 & $i(v5) & $i(v4)) | ? % 236.39/36.81 [v4: int] : ( ~ (v4 = 0) & hBOOL(v3) = v4))) % 236.39/36.81 % 236.39/36.81 (fact_2_sum__power2__eq__zero__iff) % 236.39/36.81 $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.39/36.81 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 236.39/36.81 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 236.39/36.81 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (power_power_int(v4) = v8) | ~ % 236.39/36.81 (power_power_int(v3) = v5) | ~ (plus_plus_int(v6) = v7) | ~ % 236.39/36.81 (hAPP_nat_int(v8, v2) = v9) | ~ (hAPP_nat_int(v5, v2) = v6) | ~ % 236.39/36.81 (hAPP_int_int(v7, v9) = zero_zero_int) | ~ $i(v4) | ~ $i(v3) | (v4 = % 236.39/36.81 zero_zero_int & v3 = zero_zero_int)) & ! [v3: $i] : ! [v4: $i] : ! % 236.39/36.81 [v5: $i] : ! [v6: $i] : (v6 = zero_zero_int | ~ % 236.39/36.81 (power_power_int(zero_zero_int) = v3) | ~ (plus_plus_int(v4) = v5) | ~ % 236.39/36.81 (hAPP_nat_int(v3, v2) = v4) | ~ (hAPP_int_int(v5, v4) = v6))) % 236.39/36.81 % 236.39/36.81 (fact_304_zero__less__double__add__iff__zero__less__single__add) % 236.39/36.82 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.82 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1: % 236.39/36.82 $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ? [v3: % 236.39/36.82 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.39/36.82 (plus_plus_int(v1) = v4 & hAPP_int_int(v4, v1) = v5 & hBOOL(v6) = v7 & % 236.39/36.82 hBOOL(v2) = v3 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & % 236.39/36.82 ( ~ (v3 = 0) | v7 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.39/36.82 (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 236.39/36.82 [v5: $i] : ? [v6: any] : ? [v7: any] : (plus_plus_int(v1) = v3 & % 236.39/36.82 hAPP_int_int(v3, v1) = v4 & hBOOL(v5) = v6 & hBOOL(v2) = v7 & % 236.39/36.82 hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = 0) | % 236.39/36.82 v7 = 0)))) % 236.39/36.82 % 236.39/36.82 (fact_35_zero__is__num__zero) % 236.39/36.82 number_number_of_int(pls) = zero_zero_int & $i(pls) & $i(zero_zero_int) % 236.39/36.82 % 236.39/36.82 (fact_3_sum__power2__eq__zero__iff) % 236.39/36.82 $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.39/36.82 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 236.39/36.82 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 236.39/36.82 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (plus_plus_real(v6) = v7) | ~ % 236.39/36.82 (power_power_real(v4) = v8) | ~ (power_power_real(v3) = v5) | ~ % 236.39/36.82 (hAPP_nat_real(v8, v2) = v9) | ~ (hAPP_nat_real(v5, v2) = v6) | ~ % 236.39/36.82 (hAPP_real_real(v7, v9) = zero_zero_real) | ~ $i(v4) | ~ $i(v3) | (v4 = % 236.39/36.82 zero_zero_real & v3 = zero_zero_real)) & ! [v3: $i] : ! [v4: $i] : ! % 236.39/36.82 [v5: $i] : ! [v6: $i] : (v6 = zero_zero_real | ~ (plus_plus_real(v4) = v5) % 236.39/36.82 | ~ (power_power_real(zero_zero_real) = v3) | ~ (hAPP_nat_real(v3, v2) = % 236.39/36.82 v4) | ~ (hAPP_real_real(v5, v4) = v6))) % 236.39/36.82 % 236.39/36.82 (fact_402_add__pos__pos) % 236.39/36.82 $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.82 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1: % 236.39/36.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v0, v2) % 236.39/36.82 = v3) | ~ (hAPP_int_bool(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ? % 236.39/36.82 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 236.39/36.82 [v10: any] : (plus_plus_int(v2) = v7 & hAPP_int_int(v7, v1) = v8 & % 236.39/36.82 hBOOL(v9) = v10 & hBOOL(v4) = v6 & hBOOL(v3) = v5 & hAPP_int_bool(v0, % 236.39/36.82 v8) = v9 & $i(v9) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v10 % 236.39/36.82 = 0)))) % 236.39/36.82 % 236.39/36.82 (fact_407_nat__1__add__number__of) % 236.39/36.82 $i(one_one_nat) & $i(pls) & $i(ord_less_int) & ? [v0: $i] : % 236.39/36.82 (plus_plus_nat(one_one_nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.39/36.82 (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 236.39/36.82 : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 236.39/36.82 (succ(v1) = v7 & hAPP_nat_nat(v0, v5) = v6 & number_number_of_nat(v7) = v8 % 236.39/36.82 & number_number_of_nat(v1) = v5 & hBOOL(v3) = v4 & hAPP_int_bool(v2, % 236.39/36.82 pls) = v3 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v3) & (v8 = v6 | v4 % 236.39/36.82 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.39/36.82 (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 236.39/36.82 : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : (hAPP_nat_nat(v0, v5) = v6 & % 236.39/36.82 number_number_of_nat(v1) = v5 & hBOOL(v3) = v4 & hAPP_int_bool(v2, pls) % 236.39/36.82 = v3 & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v6 = one_one_nat)))) % 236.39/36.82 % 236.39/36.82 (fact_40_int__1) % 236.39/36.82 hAPP_nat_int(semiri1621563631at_int, one_one_nat) = one_one_int & % 236.39/36.82 $i(one_one_nat) & $i(semiri1621563631at_int) & $i(one_one_int) % 236.39/36.82 % 236.39/36.82 (fact_447_zless__le) % 236.39/36.83 $i(ord_less_eq_int) & $i(ord_less_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 236.39/36.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i1948725293t_bool(ord_less_int, v0) % 236.39/36.83 = v2) | ~ (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 236.39/36.83 $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 236.39/36.83 (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v4 & hBOOL(v5) = v6 & % 236.39/36.83 hBOOL(v3) = v7 & hAPP_int_bool(v4, v1) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = % 236.39/36.83 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 236.39/36.83 : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v2) | ~ (hAPP_int_bool(v2, % 236.39/36.83 v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: % 236.39/36.83 $i] : ? [v7: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v5 & % 236.39/36.83 hBOOL(v6) = v7 & hBOOL(v3) = v4 & hAPP_int_bool(v5, v1) = v6 & $i(v6) & % 236.39/36.83 $i(v5) & ( ~ (v4 = 0) | (v7 = 0 & ~ (v1 = v0))))) % 236.39/36.83 % 236.39/36.83 (fact_45_nat__1__add__1) % 236.39/36.83 $i(one_one_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.39/36.83 $i] : (plus_plus_nat(one_one_nat) = v0 & hAPP_nat_nat(v0, one_one_nat) = v1 % 236.39/36.83 & bit1(pls) = v2 & bit0(v2) = v3 & number_number_of_nat(v3) = v1 & $i(v3) & % 236.39/36.83 $i(v2) & $i(v1) & $i(v0)) % 236.39/36.83 % 236.39/36.83 (fact_463_le__special_I2_J) % 236.39/36.83 $i(ord_less_eq_real) & $i(ord_less_eq_int) & $i(one_one_real) & $i(pls) & ? % 236.39/36.83 [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.39/36.83 (hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = v0 & bit1(pls) = v1 % 236.39/36.83 & hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2 & $i(v2) & $i(v1) & % 236.39/36.83 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ % 236.39/36.83 $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 236.39/36.83 (number267125858f_real(v3) = v6 & hBOOL(v7) = v8 & hBOOL(v4) = v5 & % 236.39/36.83 hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0))) % 236.39/36.83 & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | % 236.39/36.83 ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 236.39/36.83 (number267125858f_real(v3) = v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & % 236.39/36.83 hAPP_real_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = % 236.39/36.83 0)))) % 236.39/36.83 % 236.39/36.83 (fact_464_le__special_I2_J) % 236.39/36.83 $i(ord_less_eq_int) & $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : % 236.39/36.83 ? [v2: $i] : (bit1(pls) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, v1) = % 236.39/36.83 v2 & hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v0 & $i(v2) & % 236.39/36.83 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = % 236.39/36.83 v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 236.39/36.83 any] : (number_number_of_int(v3) = v6 & hBOOL(v7) = v8 & hBOOL(v4) = v5 % 236.39/36.83 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = % 236.39/36.83 0))) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | % 236.39/36.83 ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 236.39/36.83 (number_number_of_int(v3) = v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & % 236.39/36.84 hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = 0)))) % 236.39/36.84 % 236.39/36.84 (fact_465_le__special_I4_J) % 236.77/36.84 $i(ord_less_eq_real) & $i(ord_less_eq_int) & $i(one_one_real) & $i(pls) & ? % 236.77/36.84 [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.77/36.84 (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | ? [v3: % 236.77/36.84 $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 236.77/36.84 any] : (hAPP_r1134773055l_bool(ord_less_eq_real, v5) = v6 & % 236.77/36.84 number267125858f_real(v1) = v5 & hBOOL(v7) = v8 & hBOOL(v3) = v4 & % 236.77/36.84 hAPP_real_bool(v6, one_one_real) = v7 & hAPP_int_bool(v2, v0) = v3 & % 236.77/36.84 $i(v7) & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v8 = 0))) & ! [v1: % 236.77/36.84 $i] : ! [v2: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) % 236.77/36.84 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? % 236.77/36.84 [v7: $i] : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_eq_real, v3) = % 236.77/36.84 v4 & number267125858f_real(v1) = v3 & hBOOL(v7) = v8 & hBOOL(v5) = v6 & % 236.77/36.84 hAPP_real_bool(v4, one_one_real) = v5 & hAPP_int_bool(v2, v0) = v7 & % 236.77/36.84 $i(v7) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v8 = 0)))) % 236.77/36.84 % 236.77/36.84 (fact_466_le__special_I4_J) % 236.77/36.84 $i(ord_less_eq_int) & $i(pls) & $i(one_one_int) & ? [v0: $i] : (bit1(pls) = % 236.77/36.84 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.77/36.84 (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | ? [v3: % 236.77/36.84 $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 236.77/36.84 any] : (number_number_of_int(v1) = v5 & % 236.77/36.84 hAPP_i1948725293t_bool(ord_less_eq_int, v5) = v6 & hBOOL(v7) = v8 & % 236.77/36.84 hBOOL(v3) = v4 & hAPP_int_bool(v6, one_one_int) = v7 & hAPP_int_bool(v2, % 236.77/36.84 v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v8 = % 236.77/36.84 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.77/36.84 (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | ? [v3: % 236.77/36.84 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 236.77/36.84 any] : (number_number_of_int(v1) = v3 & % 236.77/36.84 hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4 & hBOOL(v7) = v8 & % 236.77/36.84 hBOOL(v5) = v6 & hAPP_int_bool(v4, one_one_int) = v5 & hAPP_int_bool(v2, % 236.77/36.84 v0) = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v8 = % 236.77/36.84 0)))) % 236.77/36.84 % 236.77/36.84 (fact_48_rel__simps_I2_J) % 236.77/36.84 $i(pls) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ % 236.77/36.84 (v2 = 0) & hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & hBOOL(v1) = v2 & % 236.77/36.84 hAPP_int_bool(v0, pls) = v1 & $i(v1) & $i(v0)) % 236.77/36.84 % 236.77/36.84 (fact_4_one__power2) % 236.77/36.84 $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.77/36.84 $i] : (bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 236.77/36.84 power_power_int(one_one_int) = v0 & hAPP_nat_int(v0, v3) = one_one_int & % 236.77/36.84 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.77/36.84 % 236.77/36.84 (fact_531_semiring__1__add__number__of) % 236.77/36.84 $i(ord_less_eq_int) & $i(one_one_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : % 236.77/36.84 (plus_plus_nat(one_one_nat) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.84 pls) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 236.77/36.84 (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? % 236.77/36.84 [v6: $i] : ? [v7: $i] : ? [v8: $i] : (succ(v2) = v7 & hAPP_nat_nat(v1, % 236.77/36.84 v5) = v6 & number_number_of_nat(v7) = v8 & number_number_of_nat(v2) = % 236.77/36.84 v5 & hBOOL(v3) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | % 236.77/36.84 v8 = v6)))) % 236.77/36.84 % 236.77/36.84 (fact_532_semiring__1__add__number__of) % 236.77/36.84 $i(ord_less_eq_int) & $i(pls) & $i(one_one_int) & ? [v0: $i] : ? [v1: $i] : % 236.77/36.84 (hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v0 & % 236.77/36.84 plus_plus_int(one_one_int) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 236.77/36.84 $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 236.77/36.84 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (succ(v2) = v7 & % 236.77/36.84 number_number_of_int(v7) = v8 & number_number_of_int(v2) = v5 & % 236.77/36.84 hAPP_int_int(v1, v5) = v6 & hBOOL(v3) = v4 & $i(v8) & $i(v7) & $i(v6) & % 236.77/36.84 $i(v5) & ( ~ (v4 = 0) | v8 = v6)))) % 236.77/36.84 % 236.77/36.84 (fact_538_add__pos__nonneg) % 236.77/36.85 $i(ord_less_eq_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? % 236.77/36.85 [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v1 & % 236.77/36.85 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v1) & $i(v0) & % 236.77/36.85 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 236.77/36.85 (hAPP_int_bool(v1, v2) = v5) | ~ (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) % 236.77/36.85 | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? % 236.77/36.85 [v10: $i] : ? [v11: any] : (plus_plus_int(v3) = v8 & hAPP_int_int(v8, v2) % 236.77/36.85 = v9 & hBOOL(v10) = v11 & hBOOL(v5) = v7 & hBOOL(v4) = v6 & % 236.77/36.85 hAPP_int_bool(v0, v9) = v10 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | % 236.77/36.85 ~ (v6 = 0) | v11 = 0)))) % 236.77/36.85 % 236.77/36.85 (fact_53_one__is__num__one) % 236.77/36.85 $i(pls) & $i(one_one_int) & ? [v0: $i] : (number_number_of_int(v0) = % 236.77/36.85 one_one_int & bit1(pls) = v0 & $i(v0)) % 236.77/36.85 % 236.77/36.85 (fact_541_add__nonneg__pos) % 236.77/36.85 $i(ord_less_eq_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? % 236.77/36.85 [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 236.77/36.85 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 & $i(v1) & $i(v0) & % 236.77/36.85 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 236.77/36.85 (hAPP_int_bool(v1, v2) = v5) | ~ (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) % 236.77/36.85 | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? % 236.77/36.85 [v10: $i] : ? [v11: any] : (plus_plus_int(v3) = v8 & hAPP_int_int(v8, v2) % 236.77/36.85 = v9 & hBOOL(v10) = v11 & hBOOL(v5) = v7 & hBOOL(v4) = v6 & % 236.77/36.85 hAPP_int_bool(v1, v9) = v10 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | % 236.77/36.85 ~ (v6 = 0) | v11 = 0)))) % 236.77/36.85 % 236.77/36.85 (fact_544_add__strict__increasing) % 236.77/36.85 $i(ord_less_eq_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.77/36.85 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1: % 236.77/36.85 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 236.77/36.85 : ! [v7: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ % 236.77/36.85 (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 236.77/36.85 (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: % 236.77/36.85 $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: any] : ? % 236.77/36.85 [v13: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v10 & % 236.77/36.85 hBOOL(v11) = v12 & hBOOL(v8) = v9 & hBOOL(v7) = v13 & hAPP_int_bool(v10, % 236.77/36.85 v2) = v11 & hAPP_int_bool(v0, v3) = v8 & $i(v11) & $i(v10) & $i(v8) & % 236.77/36.85 ( ~ (v12 = 0) | ~ (v9 = 0) | v13 = 0)))) % 236.77/36.85 % 236.77/36.85 (fact_547_add__strict__increasing2) % 236.77/36.85 $i(ord_less_eq_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.77/36.85 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0) & ! % 236.77/36.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 236.77/36.85 $i] : ! [v7: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | % 236.77/36.85 ~ (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 236.77/36.85 (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: % 236.77/36.85 $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 236.77/36.85 (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v7) = v12 & hAPP_int_bool(v4, % 236.77/36.85 v2) = v10 & hAPP_int_bool(v0, v3) = v8 & $i(v10) & $i(v8) & ( ~ (v11 = % 236.77/36.85 0) | ~ (v9 = 0) | v12 = 0)))) % 236.77/36.85 % 236.77/36.85 (fact_54_nat__numeral__1__eq__1) % 236.77/36.85 $i(one_one_nat) & $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & % 236.77/36.85 number_number_of_nat(v0) = one_one_nat & $i(v0)) % 236.77/36.85 % 236.77/36.85 (fact_559_rel__simps_I5_J) % 236.77/36.85 $i(ord_less_eq_int) & $i(pls) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.77/36.85 (hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v1 & % 236.77/36.85 hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & $i(v1) & $i(v0) & ! [v2: % 236.77/36.85 $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: % 236.77/36.85 any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (bit1(v2) = v5 & % 236.77/36.85 hBOOL(v6) = v7 & hBOOL(v3) = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & % 236.77/36.85 $i(v5) & ( ~ (v4 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 236.77/36.85 (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? % 236.77/36.85 [v6: any] : ? [v7: any] : (bit1(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = % 236.77/36.85 v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 = % 236.77/36.85 0)))) % 236.77/36.85 % 236.77/36.85 (fact_55_Numeral1__eq1__nat) % 236.77/36.85 $i(one_one_nat) & $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & % 236.77/36.85 number_number_of_nat(v0) = one_one_nat & $i(v0)) % 236.77/36.85 % 236.77/36.85 (fact_565_int__one__le__iff__zero__less) % 236.77/36.86 $i(ord_less_eq_int) & $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & % 236.77/36.86 ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.86 one_one_int) = v0 & hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 236.77/36.86 v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, % 236.77/36.86 v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 236.77/36.86 (hBOOL(v5) = v6 & hBOOL(v3) = v4 & hAPP_int_bool(v1, v2) = v5 & $i(v5) & ( % 236.77/36.86 ~ (v4 = 0) | v6 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 236.77/36.86 (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: any] : ? % 236.77/36.86 [v6: any] : (hBOOL(v4) = v5 & hBOOL(v3) = v6 & hAPP_int_bool(v1, v2) = v4 % 236.77/36.86 & $i(v4) & ( ~ (v5 = 0) | v6 = 0)))) % 236.77/36.86 % 236.77/36.86 (fact_567_succ__Pls) % 236.77/36.86 $i(pls) & ? [v0: $i] : (succ(pls) = v0 & bit1(pls) = v0 & $i(v0)) % 236.77/36.86 % 236.77/36.86 (fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) % 236.77/36.86 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.77/36.86 : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (number_number_of_int(v2) = v3 & % 236.77/36.86 bit1(v1) = v2 & bit1(pls) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.86 zero_zero_int) = v0 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) % 236.77/36.86 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.77/36.86 % 236.77/36.86 (fact_581_le__imp__0__less) % 236.77/36.86 $i(ord_less_eq_int) & $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & % 236.77/36.86 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.77/36.86 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 236.77/36.86 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 & % 236.77/36.86 plus_plus_int(one_one_int) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : % 236.77/36.86 ! [v4: $i] : ( ~ (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) | ? [v5: any] : % 236.77/36.86 ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (hAPP_int_int(v2, v3) = v6 & % 236.77/36.86 hBOOL(v7) = v8 & hBOOL(v4) = v5 & hAPP_int_bool(v1, v6) = v7 & $i(v7) & % 236.77/36.86 $i(v6) & ( ~ (v5 = 0) | v8 = 0)))) % 236.77/36.86 % 236.77/36.86 (fact_583_number__of__succ) % 236.77/36.86 $i(one_one_int) & ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! % 236.77/36.86 [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? % 236.77/36.86 [v4: $i] : (number_number_of_int(v2) = v3 & number_number_of_int(v1) = v4 % 236.77/36.86 & hAPP_int_int(v0, v4) = v3 & $i(v4) & $i(v3)))) % 236.77/36.86 % 236.77/36.86 (fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) % 236.77/36.86 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.77/36.86 : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (number_number_of_int(v2) = v3 & % 236.77/36.86 bit1(pls) = v1 & bit0(v1) = v2 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.86 zero_zero_int) = v0 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) % 236.77/36.86 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.77/36.86 % 236.77/36.86 (fact_589_power2__ge__self) % 236.77/36.86 $i(ord_less_eq_int) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.77/36.86 (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v2) & % 236.77/36.86 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 236.77/36.86 [v7: $i] : ( ~ (power_power_int(v3) = v5) | ~ % 236.77/36.86 (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4) | ~ (hAPP_nat_int(v5, % 236.77/36.86 v2) = v6) | ~ (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | hBOOL(v7) = % 236.77/36.86 0)) % 236.77/36.86 % 236.77/36.86 (fact_590_zero__le__power2) % 236.77/36.86 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.77/36.86 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 236.77/36.86 zero_zero_real) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 236.77/36.86 number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.77/36.86 $i] : ! [v5: $i] : ( ~ (power_power_real(v4) = v5) | ~ $i(v4) | ? [v6: % 236.77/36.86 $i] : ? [v7: $i] : (hAPP_nat_real(v5, v3) = v6 & hBOOL(v7) = 0 & % 236.77/36.86 hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6)))) % 236.77/36.86 % 236.77/36.86 (fact_591_zero__le__power2) % 236.77/36.86 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.77/36.86 : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 & bit0(v1) = v2 & % 236.77/36.86 number_number_of_nat(v2) = v3 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.86 zero_zero_int) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 236.77/36.86 [v5: $i] : ( ~ (power_power_int(v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? % 236.77/36.86 [v7: $i] : (hAPP_nat_int(v5, v3) = v6 & hBOOL(v7) = 0 & hAPP_int_bool(v0, % 236.77/36.86 v6) = v7 & $i(v7) & $i(v6)))) % 236.77/36.86 % 236.77/36.86 (fact_592_power2__le__imp__le) % 236.77/36.86 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.77/36.86 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 236.77/36.86 zero_zero_real) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.86 number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.77/36.86 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 236.77/36.86 : ! [v10: $i] : ! [v11: $i] : ( ~ % 236.77/36.86 (hAPP_r1134773055l_bool(ord_less_eq_real, v7) = v8) | ~ % 236.77/36.86 (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 236.77/36.86 (hAPP_nat_real(v9, v2) = v10) | ~ (hAPP_nat_real(v6, v2) = v7) | ~ % 236.77/36.86 (hAPP_real_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: any] : % 236.77/36.86 ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17: any] % 236.77/36.86 : (hAPP_r1134773055l_bool(ord_less_eq_real, v4) = v15 & hBOOL(v16) = v17 & % 236.77/36.86 hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_real_bool(v15, v5) = v16 & % 236.77/36.86 hAPP_real_bool(v3, v5) = v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = % 236.77/36.86 0) | ~ (v12 = 0) | v17 = 0)))) % 236.77/36.86 % 236.77/36.86 (fact_593_power2__le__imp__le) % 236.77/36.87 $i(ord_less_eq_nat) & $i(zero_zero_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] % 236.77/36.87 : ? [v2: $i] : ? [v3: $i] : (hAPP_n1699378549t_bool(ord_less_eq_nat, % 236.77/36.87 zero_zero_nat) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.87 number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.77/36.87 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 236.77/36.87 : ! [v10: $i] : ! [v11: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_eq_nat, % 236.77/36.87 v7) = v8) | ~ (power_power_nat(v5) = v9) | ~ (power_power_nat(v4) = % 236.77/36.87 v6) | ~ (hAPP_nat_nat(v9, v2) = v10) | ~ (hAPP_nat_nat(v6, v2) = v7) | % 236.77/36.87 ~ (hAPP_nat_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: any] % 236.77/36.87 : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17: % 236.77/36.87 any] : (hAPP_n1699378549t_bool(ord_less_eq_nat, v4) = v15 & hBOOL(v16) = % 236.77/36.87 v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_nat_bool(v15, v5) = v16 % 236.77/36.87 & hAPP_nat_bool(v3, v5) = v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = % 236.77/36.87 0) | ~ (v12 = 0) | v17 = 0)))) % 236.77/36.87 % 236.77/36.87 (fact_594_power2__le__imp__le) % 236.77/36.87 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.77/36.87 : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.87 number_number_of_nat(v1) = v2 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.87 zero_zero_int) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 236.77/36.87 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 236.77/36.87 $i] : ! [v11: $i] : ( ~ (power_power_int(v5) = v9) | ~ % 236.77/36.87 (power_power_int(v4) = v6) | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.87 v7) = v8) | ~ (hAPP_nat_int(v9, v2) = v10) | ~ (hAPP_nat_int(v6, v2) % 236.77/36.87 = v7) | ~ (hAPP_int_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 236.77/36.87 [v12: any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : % 236.77/36.87 ? [v17: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, v4) = v15 & % 236.77/36.87 hBOOL(v16) = v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & % 236.77/36.87 hAPP_int_bool(v15, v5) = v16 & hAPP_int_bool(v3, v5) = v13 & $i(v16) & % 236.77/36.87 $i(v15) & $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 = 0)))) % 236.77/36.87 % 236.77/36.87 (fact_595_power2__eq__imp__eq) % 236.77/36.87 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.77/36.87 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 236.77/36.87 zero_zero_real) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.87 number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.77/36.87 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ % 236.77/36.87 (hAPP_real_bool(v3, v5) = v7) | ~ (hAPP_real_bool(v3, v4) = v6) | ~ % 236.77/36.87 $i(v5) | ~ $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 236.77/36.87 $i] : ? [v12: any] : ? [v13: any] : (power_power_real(v5) = v10 & % 236.77/36.87 power_power_real(v4) = v8 & hAPP_nat_real(v10, v2) = v11 & % 236.77/36.87 hAPP_nat_real(v8, v2) = v9 & hBOOL(v7) = v13 & hBOOL(v6) = v12 & $i(v11) % 236.77/36.87 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = % 236.77/36.87 v9))))) % 236.77/36.87 % 236.77/36.87 (fact_596_power2__eq__imp__eq) % 236.77/36.87 $i(ord_less_eq_nat) & $i(zero_zero_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] % 236.77/36.87 : ? [v2: $i] : ? [v3: $i] : (hAPP_n1699378549t_bool(ord_less_eq_nat, % 236.77/36.87 zero_zero_nat) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.87 number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.77/36.87 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ % 236.77/36.87 (hAPP_nat_bool(v3, v5) = v7) | ~ (hAPP_nat_bool(v3, v4) = v6) | ~ $i(v5) % 236.77/36.87 | ~ $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 236.77/36.87 [v12: any] : ? [v13: any] : (power_power_nat(v5) = v10 & % 236.77/36.87 power_power_nat(v4) = v8 & hAPP_nat_nat(v10, v2) = v11 & % 236.77/36.87 hAPP_nat_nat(v8, v2) = v9 & hBOOL(v7) = v13 & hBOOL(v6) = v12 & $i(v11) % 236.77/36.87 & $i(v10) & $i(v9) & $i(v8) & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = % 236.77/36.87 v9))))) % 236.77/36.87 % 236.77/36.87 (fact_597_power2__eq__imp__eq) % 236.77/36.87 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.77/36.87 : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & % 236.77/36.87 number_number_of_nat(v1) = v2 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.77/36.87 zero_zero_int) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 236.77/36.87 [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (hAPP_int_bool(v3, v5) % 236.77/36.87 = v7) | ~ (hAPP_int_bool(v3, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ? % 236.77/36.87 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: any] : ? % 236.77/36.87 [v13: any] : (power_power_int(v5) = v10 & power_power_int(v4) = v8 & % 236.77/36.87 hAPP_nat_int(v10, v2) = v11 & hAPP_nat_int(v8, v2) = v9 & hBOOL(v7) = % 236.77/36.87 v13 & hBOOL(v6) = v12 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v13 = % 236.77/36.87 0) | ~ (v12 = 0) | ~ (v11 = v9))))) % 236.77/36.87 % 236.77/36.87 (fact_5_one__power2) % 236.94/36.87 $i(one_one_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.94/36.87 $i] : (power_power_nat(one_one_nat) = v0 & hAPP_nat_nat(v0, v3) = % 236.94/36.87 one_one_nat & bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 % 236.94/36.87 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.87 % 236.94/36.87 (fact_600_power2__less__imp__less) % 236.94/36.87 $i(ord_less_eq_real) & $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & ? % 236.94/36.87 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.87 (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v3 & bit1(pls) = % 236.94/36.87 v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & % 236.94/36.87 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 236.94/36.87 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 236.94/36.87 (hAPP_r1134773055l_bool(ord_less_real, v7) = v8) | ~ % 236.94/36.87 (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 236.94/36.87 (hAPP_nat_real(v9, v2) = v10) | ~ (hAPP_nat_real(v6, v2) = v7) | ~ % 236.94/36.87 (hAPP_real_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: any] : % 236.94/36.87 ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17: any] % 236.94/36.87 : (hAPP_r1134773055l_bool(ord_less_real, v4) = v15 & hBOOL(v16) = v17 & % 236.94/36.87 hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_real_bool(v15, v5) = v16 & % 236.94/36.87 hAPP_real_bool(v3, v5) = v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = % 236.94/36.87 0) | ~ (v12 = 0) | v17 = 0)))) % 236.94/36.87 % 236.94/36.87 (fact_601_power2__less__imp__less) % 236.94/36.88 $i(ord_less_eq_nat) & $i(ord_less_nat) & $i(zero_zero_nat) & $i(pls) & ? [v0: % 236.94/36.88 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.88 (hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = v3 & bit1(pls) = v0 % 236.94/36.88 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & % 236.94/36.88 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 236.94/36.88 : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 236.94/36.88 (hAPP_n1699378549t_bool(ord_less_nat, v7) = v8) | ~ (power_power_nat(v5) % 236.94/36.88 = v9) | ~ (power_power_nat(v4) = v6) | ~ (hAPP_nat_nat(v9, v2) = v10) % 236.94/36.88 | ~ (hAPP_nat_nat(v6, v2) = v7) | ~ (hAPP_nat_bool(v8, v10) = v11) | ~ % 236.94/36.88 $i(v5) | ~ $i(v4) | ? [v12: any] : ? [v13: $i] : ? [v14: any] : ? % 236.94/36.88 [v15: $i] : ? [v16: $i] : ? [v17: any] : % 236.94/36.88 (hAPP_n1699378549t_bool(ord_less_nat, v4) = v15 & hBOOL(v16) = v17 & % 236.94/36.88 hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_nat_bool(v15, v5) = v16 & % 236.94/36.88 hAPP_nat_bool(v3, v5) = v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = % 236.94/36.88 0) | ~ (v12 = 0) | v17 = 0)))) % 236.94/36.88 % 236.94/36.88 (fact_602_power2__less__imp__less) % 236.94/36.88 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: % 236.94/36.88 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v0 & bit0(v0) = % 236.94/36.88 v1 & number_number_of_nat(v1) = v2 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.94/36.88 zero_zero_int) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 236.94/36.88 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 236.94/36.88 $i] : ! [v11: $i] : ( ~ (power_power_int(v5) = v9) | ~ % 236.94/36.88 (power_power_int(v4) = v6) | ~ (hAPP_i1948725293t_bool(ord_less_int, v7) % 236.94/36.88 = v8) | ~ (hAPP_nat_int(v9, v2) = v10) | ~ (hAPP_nat_int(v6, v2) = v7) % 236.94/36.88 | ~ (hAPP_int_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: % 236.94/36.88 any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? % 236.94/36.88 [v17: any] : (hAPP_i1948725293t_bool(ord_less_int, v4) = v15 & hBOOL(v16) % 236.94/36.88 = v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_int_bool(v15, v5) = % 236.94/36.88 v16 & hAPP_int_bool(v3, v5) = v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ % 236.94/36.88 (v14 = 0) | ~ (v12 = 0) | v17 = 0)))) % 236.94/36.88 % 236.94/36.88 (fact_603_sum__power2__ge__zero) % 236.94/36.88 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.94/36.88 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 236.94/36.88 zero_zero_real) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.88 number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.94/36.88 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 236.94/36.88 : ! [v10: $i] : ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 236.94/36.88 (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 236.94/36.88 (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | ~ % 236.94/36.88 (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 236.94/36.88 (hBOOL(v12) = 0 & hAPP_real_bool(v0, v11) = v12 & $i(v12)))) % 236.94/36.88 % 236.94/36.88 (fact_604_sum__power2__ge__zero) % 236.94/36.88 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.94/36.88 : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.88 number_number_of_nat(v2) = v3 & hAPP_i1948725293t_bool(ord_less_eq_int, % 236.94/36.88 zero_zero_int) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! % 236.94/36.88 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 236.94/36.88 $i] : ! [v11: $i] : ( ~ (power_power_int(v5) = v9) | ~ % 236.94/36.88 (power_power_int(v4) = v6) | ~ (plus_plus_int(v7) = v8) | ~ % 236.94/36.88 (hAPP_nat_int(v9, v3) = v10) | ~ (hAPP_nat_int(v6, v3) = v7) | ~ % 236.94/36.88 (hAPP_int_int(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 236.94/36.88 (hBOOL(v12) = 0 & hAPP_int_bool(v0, v11) = v12 & $i(v12)))) % 236.94/36.88 % 236.94/36.88 (fact_605_sum__power2__le__zero__iff) % 236.94/36.88 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.94/36.88 $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & % 236.94/36.88 number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 236.94/36.88 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: % 236.94/36.88 $i] : ! [v10: $i] : ( ~ (plus_plus_real(v6) = v7) | ~ % 236.94/36.88 (power_power_real(v4) = v8) | ~ (power_power_real(v3) = v5) | ~ % 236.94/36.88 (hAPP_nat_real(v8, v2) = v9) | ~ (hAPP_nat_real(v5, v2) = v6) | ~ % 236.94/36.88 (hAPP_real_real(v7, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ? [v11: $i] : ? % 236.94/36.88 [v12: $i] : ? [v13: int] : ( ~ (v13 = 0) & % 236.94/36.88 hAPP_r1134773055l_bool(ord_less_eq_real, v10) = v11 & hBOOL(v12) = v13 & % 236.94/36.88 hAPP_real_bool(v11, zero_zero_real) = v12 & $i(v12) & $i(v11)) | (v4 = % 236.94/36.88 zero_zero_real & v3 = zero_zero_real)) & ! [v3: $i] : ! [v4: $i] : ! % 236.94/36.88 [v5: $i] : ! [v6: $i] : ( ~ (plus_plus_real(v4) = v5) | ~ % 236.94/36.88 (power_power_real(zero_zero_real) = v3) | ~ (hAPP_nat_real(v3, v2) = v4) % 236.94/36.88 | ~ (hAPP_real_real(v5, v4) = v6) | ? [v7: $i] : ? [v8: $i] : % 236.94/36.88 (hAPP_r1134773055l_bool(ord_less_eq_real, v6) = v7 & hBOOL(v8) = 0 & % 236.94/36.88 hAPP_real_bool(v7, zero_zero_real) = v8 & $i(v8) & $i(v7)))) % 236.94/36.88 % 236.94/36.88 (fact_606_sum__power2__le__zero__iff) % 236.94/36.88 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.94/36.88 : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = % 236.94/36.88 v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 236.94/36.88 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 236.94/36.88 (power_power_int(v4) = v8) | ~ (power_power_int(v3) = v5) | ~ % 236.94/36.88 (plus_plus_int(v6) = v7) | ~ (hAPP_nat_int(v8, v2) = v9) | ~ % 236.94/36.88 (hAPP_nat_int(v5, v2) = v6) | ~ (hAPP_int_int(v7, v9) = v10) | ~ $i(v4) % 236.94/36.88 | ~ $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: int] : ( ~ (v13 = 0) % 236.94/36.88 & hAPP_i1948725293t_bool(ord_less_eq_int, v10) = v11 & hBOOL(v12) = v13 % 236.94/36.88 & hAPP_int_bool(v11, zero_zero_int) = v12 & $i(v12) & $i(v11)) | (v4 = % 236.94/36.88 zero_zero_int & v3 = zero_zero_int)) & ! [v3: $i] : ! [v4: $i] : ! % 236.94/36.88 [v5: $i] : ! [v6: $i] : ( ~ (power_power_int(zero_zero_int) = v3) | ~ % 236.94/36.88 (plus_plus_int(v4) = v5) | ~ (hAPP_nat_int(v3, v2) = v4) | ~ % 236.94/36.88 (hAPP_int_int(v5, v4) = v6) | ? [v7: $i] : ? [v8: $i] : % 236.94/36.88 (hAPP_i1948725293t_bool(ord_less_eq_int, v6) = v7 & hBOOL(v8) = 0 & % 236.94/36.88 hAPP_int_bool(v7, zero_zero_int) = v8 & $i(v8) & $i(v7)))) % 236.94/36.88 % 236.94/36.88 (fact_607_int__pos__lt__two__imp__zero__or__one) % 236.94/36.89 $i(ord_less_eq_int) & $i(pls) & $i(one_one_int) & $i(zero_zero_int) & % 236.94/36.89 $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.89 (number_number_of_int(v2) = v3 & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.89 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v3) & % 236.94/36.89 $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v4 = one_one_int | % 236.94/36.89 v4 = zero_zero_int | ~ (hAPP_int_bool(v0, v4) = v5) | ~ $i(v4) | ? [v6: % 236.94/36.89 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : % 236.94/36.89 (hAPP_i1948725293t_bool(ord_less_int, v4) = v7 & hBOOL(v8) = v9 & % 236.94/36.89 hBOOL(v5) = v6 & hAPP_int_bool(v7, v3) = v8 & $i(v8) & $i(v7) & ( ~ (v9 % 236.94/36.89 = 0) | ~ (v6 = 0))))) % 236.94/36.89 % 236.94/36.89 (fact_609_number__of2) % 236.94/36.89 $i(ord_less_eq_int) & $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] % 236.94/36.89 : ? [v2: $i] : (number_number_of_int(pls) = v1 & % 236.94/36.89 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & hBOOL(v2) = 0 % 236.94/36.89 & hAPP_int_bool(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.89 % 236.94/36.89 (fact_642_two__realpow__ge__one) % 236.94/36.89 $i(ord_less_eq_real) & $i(one_one_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] % 236.94/36.89 : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 236.94/36.89 (hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = v0 & % 236.94/36.89 number267125858f_real(v2) = v3 & power_power_real(v3) = v4 & bit1(pls) = v1 % 236.94/36.89 & bit0(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : % 236.94/36.89 ! [v6: $i] : ( ~ (hAPP_nat_real(v4, v5) = v6) | ~ $i(v5) | ? [v7: $i] : % 236.94/36.89 (hBOOL(v7) = 0 & hAPP_real_bool(v0, v6) = v7 & $i(v7)))) % 236.94/36.89 % 236.94/36.89 (fact_645_ex__least__nat__less) % 236.94/36.89 $i(ord_less_eq_nat) & $i(ord_less_nat) & $i(zero_zero_nat) & $i(one_one_nat) & % 236.94/36.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_nat_bool(v1, v0) = v2) | % 236.94/36.89 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 236.94/36.89 : ? [v7: $i] : ? [v8: $i] : (hAPP_n1699378549t_bool(ord_less_nat, v3) = v4 % 236.94/36.89 & plus_plus_nat(v3) = v6 & hAPP_nat_nat(v6, one_one_nat) = v7 & hBOOL(v8) % 236.94/36.89 = 0 & hBOOL(v5) = 0 & hAPP_nat_bool(v4, v0) = v5 & hAPP_nat_bool(v1, v7) = % 236.94/36.89 v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ! [v9: $i] : % 236.94/36.89 ! [v10: $i] : ! [v11: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_eq_nat, % 236.94/36.89 v9) = v10) | ~ (hAPP_nat_bool(v10, v3) = v11) | ~ $i(v9) | ? % 236.94/36.89 [v12: any] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & % 236.94/36.89 hBOOL(v11) = v12 & hAPP_nat_bool(v1, v9) = v13 & $i(v13) & ( ~ (v14 = % 236.94/36.89 0) | ~ (v12 = 0))))) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 236.94/36.89 : (hBOOL(v3) = v4 & hBOOL(v2) = v5 & hAPP_nat_bool(v1, zero_zero_nat) = v3 & % 236.94/36.89 $i(v3) & ( ~ (v5 = 0) | v4 = 0))) % 236.94/36.89 % 236.94/36.89 (fact_690_real__sqrt__sum__squares__ge__zero) % 236.94/36.89 $i(ord_less_eq_real) & $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: % 236.94/36.89 $i] : ? [v2: $i] : ? [v3: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 236.94/36.89 zero_zero_real) = v0 & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.89 number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.94/36.89 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 236.94/36.89 : ! [v10: $i] : ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 236.94/36.89 (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 236.94/36.89 (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | ~ % 236.94/36.89 (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 236.94/36.89 ? [v13: $i] : (sqrt(v11) = v12 & hBOOL(v13) = 0 & hAPP_real_bool(v0, v12) % 236.94/36.89 = v13 & $i(v13) & $i(v12)))) % 236.94/36.89 % 236.94/36.89 (fact_691_zadd__power2) % 236.94/36.89 $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.89 (number_number_of_int(v1) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 236.94/36.89 number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 236.94/36.89 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 236.94/36.89 : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : % 236.94/36.89 ! [v15: $i] : ( ~ (times_times_int(v9, v5) = v10) | ~ (times_times_int(v3, % 236.94/36.89 v4) = v9) | ~ (power_power_int(v5) = v13) | ~ (power_power_int(v4) = % 236.94/36.89 v6) | ~ (plus_plus_int(v11) = v12) | ~ (plus_plus_int(v7) = v8) | ~ % 236.94/36.89 (hAPP_nat_int(v13, v2) = v14) | ~ (hAPP_nat_int(v6, v2) = v7) | ~ % 236.94/36.89 (hAPP_int_int(v12, v14) = v15) | ~ (hAPP_int_int(v8, v10) = v11) | ~ % 236.94/36.89 $i(v5) | ~ $i(v4) | ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 236.94/36.89 (power_power_int(v17) = v18 & plus_plus_int(v4) = v16 & hAPP_nat_int(v18, % 236.94/36.89 v2) = v15 & hAPP_int_int(v16, v5) = v17 & $i(v18) & $i(v17) & $i(v16) % 236.94/36.89 & $i(v15)))) % 236.94/36.89 % 236.94/36.89 (fact_6_one__power2) % 236.94/36.89 $i(one_one_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 236.94/36.89 $i] : (power_power_real(one_one_real) = v0 & hAPP_nat_real(v0, v3) = % 236.94/36.89 one_one_real & bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = % 236.94/36.89 v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.89 % 236.94/36.89 (fact_71_less__special_I1_J) % 236.94/36.89 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.94/36.89 (hAPP_i1948725293t_bool(ord_less_int, pls) = v1 & % 236.94/36.89 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v1) & $i(v0) & % 236.94/36.89 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | % 236.94/36.89 ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.94/36.89 (number_number_of_int(v2) = v5 & hBOOL(v6) = v7 & hBOOL(v3) = v4 & % 236.94/36.89 hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = 0))) % 236.94/36.89 & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | % 236.94/36.89 ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 236.94/36.89 (number_number_of_int(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & % 236.94/36.89 hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 236.94/36.89 % 236.94/36.89 (fact_72_less__special_I1_J) % 236.94/36.90 $i(ord_less_real) & $i(zero_zero_real) & $i(pls) & $i(ord_less_int) & ? [v0: % 236.94/36.90 $i] : ? [v1: $i] : (hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = % 236.94/36.90 v0 & hAPP_i1948725293t_bool(ord_less_int, pls) = v1 & $i(v1) & $i(v0) & ! % 236.94/36.90 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? % 236.94/36.90 [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 236.94/36.90 (number267125858f_real(v2) = v5 & hBOOL(v6) = v7 & hBOOL(v3) = v4 & % 236.94/36.90 hAPP_real_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = 0))) % 236.94/36.90 & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | % 236.94/36.90 ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 236.94/36.90 (number267125858f_real(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & % 236.94/36.90 hAPP_real_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 = % 236.94/36.90 0)))) % 236.94/36.90 % 236.94/36.90 (fact_77_rel__simps_I4_J) % 236.94/36.90 $i(pls) & $i(ord_less_int) & ? [v0: $i] : % 236.94/36.90 (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & $i(v0) & ! [v1: $i] : ! % 236.94/36.90 [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 236.94/36.90 [v4: $i] : ? [v5: $i] : ? [v6: any] : (bit0(v1) = v4 & hBOOL(v5) = v6 & % 236.94/36.90 hBOOL(v2) = v3 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v3 % 236.94/36.90 = 0) | v6 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.94/36.90 (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? % 236.94/36.90 [v5: any] : ? [v6: any] : (bit0(v1) = v3 & hBOOL(v4) = v5 & hBOOL(v2) = % 236.94/36.90 v6 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v5 = 0) | v6 = % 236.94/36.90 0)))) % 236.94/36.90 % 236.94/36.90 (fact_79_bin__less__0__simps_I1_J) % 236.94/36.90 $i(pls) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : % 236.94/36.90 ? [v2: int] : ( ~ (v2 = 0) & hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & % 236.94/36.90 hBOOL(v1) = v2 & hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0)) % 236.94/36.90 % 236.94/36.90 (fact_7_zero__power2) % 236.94/36.90 $i(pls) & $i(zero_zero_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 236.94/36.90 [v3: $i] : (bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 236.94/36.90 power_power_int(zero_zero_int) = v0 & hAPP_nat_int(v0, v3) = zero_zero_int & % 236.94/36.90 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.90 % 236.94/36.90 (fact_81_int__0__less__1) % 236.94/36.90 $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: % 236.94/36.90 $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & hBOOL(v1) % 236.94/36.90 = 0 & hAPP_int_bool(v0, one_one_int) = v1 & $i(v1) & $i(v0)) % 236.94/36.90 % 236.94/36.90 (fact_84_less__special_I4_J) % 236.94/36.90 $i(pls) & $i(one_one_int) & $i(ord_less_int) & ? [v0: $i] : (bit1(pls) = v0 & % 236.94/36.90 $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.94/36.90 (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 236.94/36.90 : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 236.94/36.90 (number_number_of_int(v1) = v5 & hAPP_i1948725293t_bool(ord_less_int, v5) % 236.94/36.90 = v6 & hBOOL(v7) = v8 & hBOOL(v3) = v4 & hAPP_int_bool(v6, one_one_int) % 236.94/36.90 = v7 & hAPP_int_bool(v2, v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & % 236.94/36.90 ( ~ (v4 = 0) | v8 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.94/36.90 (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 236.94/36.90 : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 236.94/36.90 (number_number_of_int(v1) = v3 & hAPP_i1948725293t_bool(ord_less_int, v3) % 236.94/36.90 = v4 & hBOOL(v7) = v8 & hBOOL(v5) = v6 & hAPP_int_bool(v4, one_one_int) % 236.94/36.90 = v5 & hAPP_int_bool(v2, v0) = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 236.94/36.90 ( ~ (v6 = 0) | v8 = 0)))) % 236.94/36.90 % 236.94/36.90 (fact_85_less__special_I4_J) % 236.94/36.90 $i(ord_less_real) & $i(one_one_real) & $i(pls) & $i(ord_less_int) & ? [v0: % 236.94/36.90 $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 236.94/36.90 (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? [v3: $i] % 236.94/36.90 : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 236.94/36.90 (hAPP_r1134773055l_bool(ord_less_real, v5) = v6 & % 236.94/36.90 number267125858f_real(v1) = v5 & hBOOL(v7) = v8 & hBOOL(v3) = v4 & % 236.94/36.90 hAPP_real_bool(v6, one_one_real) = v7 & hAPP_int_bool(v2, v0) = v3 & % 236.94/36.90 $i(v7) & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v8 = 0))) & ! [v1: % 236.94/36.90 $i] : ! [v2: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | % 236.94/36.90 ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? % 236.94/36.90 [v7: $i] : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_real, v3) = v4 % 236.94/36.90 & number267125858f_real(v1) = v3 & hBOOL(v7) = v8 & hBOOL(v5) = v6 & % 236.94/36.90 hAPP_real_bool(v4, one_one_real) = v5 & hAPP_int_bool(v2, v0) = v7 & % 236.94/36.90 $i(v7) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v8 = 0)))) % 236.94/36.90 % 236.94/36.90 (fact_86_less__special_I2_J) % 236.94/36.90 $i(pls) & $i(one_one_int) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] : ? % 236.94/36.90 [v2: $i] : (bit1(pls) = v1 & hAPP_i1948725293t_bool(ord_less_int, v1) = v2 & % 236.94/36.90 hAPP_i1948725293t_bool(ord_less_int, one_one_int) = v0 & $i(v2) & $i(v1) & % 236.94/36.90 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ % 236.94/36.90 $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 236.94/36.90 (number_number_of_int(v3) = v6 & hBOOL(v7) = v8 & hBOOL(v4) = v5 & % 236.94/36.90 hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0))) % 236.94/36.90 & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | % 236.94/36.90 ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 236.94/36.90 (number_number_of_int(v3) = v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & % 236.94/36.90 hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = 0)))) % 236.94/36.90 % 236.94/36.90 (fact_87_less__special_I2_J) % 236.94/36.90 $i(ord_less_real) & $i(one_one_real) & $i(pls) & $i(ord_less_int) & ? [v0: % 236.94/36.90 $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_r1134773055l_bool(ord_less_real, % 236.94/36.90 one_one_real) = v0 & bit1(pls) = v1 & hAPP_i1948725293t_bool(ord_less_int, % 236.94/36.90 v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 236.94/36.90 (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? % 236.94/36.90 [v7: $i] : ? [v8: any] : (number267125858f_real(v3) = v6 & hBOOL(v7) = v8 % 236.94/36.90 & hBOOL(v4) = v5 & hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ % 236.94/36.90 (v5 = 0) | v8 = 0))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 236.94/36.90 (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? % 236.94/36.90 [v7: any] : ? [v8: any] : (number267125858f_real(v3) = v5 & hBOOL(v6) = % 236.94/36.90 v7 & hBOOL(v4) = v8 & hAPP_real_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( % 236.94/36.91 ~ (v7 = 0) | v8 = 0)))) % 236.94/36.91 % 236.94/36.91 (fact_88_odd__less__0) % 236.94/36.91 $i(one_one_int) & $i(zero_zero_int) & $i(ord_less_int) & ? [v0: $i] : % 236.94/36.91 (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! % 236.94/36.91 [v3: $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) = v3) | ~ (hAPP_int_int(v3, % 236.94/36.91 v1) = v4) | ~ (hAPP_int_int(v0, v1) = v2) | ~ $i(v1) | ? [v5: $i] : % 236.94/36.91 ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : % 236.94/36.91 (hAPP_i1948725293t_bool(ord_less_int, v4) = v8 & % 236.94/36.91 hAPP_i1948725293t_bool(ord_less_int, v1) = v5 & hBOOL(v9) = v10 & % 236.94/36.91 hBOOL(v6) = v7 & hAPP_int_bool(v8, zero_zero_int) = v9 & % 236.94/36.91 hAPP_int_bool(v5, zero_zero_int) = v6 & $i(v9) & $i(v8) & $i(v6) & % 236.94/36.91 $i(v5) & ( ~ (v7 = 0) | v10 = 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 236.94/36.91 $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) = v3) | ~ (hAPP_int_int(v3, % 236.94/36.91 v1) = v4) | ~ (hAPP_int_int(v0, v1) = v2) | ~ $i(v1) | ? [v5: $i] : % 236.94/36.91 ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : % 236.94/36.91 (hAPP_i1948725293t_bool(ord_less_int, v4) = v5 & % 236.94/36.91 hAPP_i1948725293t_bool(ord_less_int, v1) = v8 & hBOOL(v9) = v10 & % 236.94/36.91 hBOOL(v6) = v7 & hAPP_int_bool(v8, zero_zero_int) = v9 & % 236.94/36.91 hAPP_int_bool(v5, zero_zero_int) = v6 & $i(v9) & $i(v8) & $i(v6) & % 236.94/36.91 $i(v5) & ( ~ (v7 = 0) | v10 = 0)))) % 236.94/36.91 % 236.94/36.91 (fact_8_zero__power2) % 236.94/36.91 $i(zero_zero_nat) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 236.94/36.91 [v3: $i] : (power_power_nat(zero_zero_nat) = v0 & hAPP_nat_nat(v0, v3) = % 236.94/36.91 zero_zero_nat & bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = % 236.94/36.91 v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.91 % 236.94/36.91 (fact_98_Pls__def) % 236.94/36.91 pls = zero_zero_int & $i(zero_zero_int) % 236.94/36.91 % 236.94/36.91 (fact_9_zero__power2) % 236.94/36.91 $i(zero_zero_real) & $i(pls) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 236.94/36.91 [v3: $i] : (power_power_real(zero_zero_real) = v0 & hAPP_nat_real(v0, v3) = % 236.94/36.91 zero_zero_real & bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = % 236.94/36.91 v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.91 % 236.94/36.91 (function-axioms) % 236.94/36.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 236.94/36.92 (times_times_int(v3, v2) = v1) | ~ (times_times_int(v3, v2) = v0)) & ! % 236.94/36.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (if_nat(v3, % 236.94/36.92 v2) = v1) | ~ (if_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 236.94/36.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_r1134773055l_bool(v3, v2) = v1) | % 236.94/36.92 ~ (hAPP_r1134773055l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 236.94/36.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1699378549t_bool(v3, v2) = v1) | % 236.94/36.92 ~ (hAPP_n1699378549t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 236.94/36.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_nat(v3, v2) = v1) | ~ % 236.94/36.92 (hAPP_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 236.94/36.92 [v3: $i] : (v1 = v0 | ~ (hAPP_nat_real(v3, v2) = v1) | ~ (hAPP_nat_real(v3, % 236.94/36.92 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 236.94/36.92 = v0 | ~ (hAPP_real_real(v3, v2) = v1) | ~ (hAPP_real_real(v3, v2) = v0)) % 236.94/36.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 236.94/36.92 (hAPP_i1948725293t_bool(v3, v2) = v1) | ~ (hAPP_i1948725293t_bool(v3, v2) = % 236.94/36.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 236.94/36.92 ~ (hAPP_nat_int(v3, v2) = v1) | ~ (hAPP_nat_int(v3, v2) = v0)) & ! [v0: % 236.94/36.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 236.94/36.92 (hAPP_int_int(v3, v2) = v1) | ~ (hAPP_int_int(v3, v2) = v0)) & ! [v0: $i] % 236.94/36.92 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_real_bool(v3, % 236.94/36.92 v2) = v1) | ~ (hAPP_real_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 236.94/36.92 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_bool(v3, v2) = v1) % 236.94/36.92 | ~ (hAPP_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 236.94/36.92 : ! [v3: $i] : (v1 = v0 | ~ (hAPP_int_bool(v3, v2) = v1) | ~ % 236.94/36.92 (hAPP_int_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 236.94/36.92 (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & ! [v0: $i] : ! [v1: % 236.94/36.92 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! % 236.94/36.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (plus_plus_nat(v2) = v1) % 236.94/36.92 | ~ (plus_plus_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 236.94/36.92 (v1 = v0 | ~ (number267125858f_real(v2) = v1) | ~ (number267125858f_real(v2) % 236.94/36.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 236.94/36.92 (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) = v0)) & ! % 236.94/36.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_power_nat(v2) = % 236.94/36.92 v1) | ~ (power_power_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 236.94/36.92 $i] : (v1 = v0 | ~ (plus_plus_real(v2) = v1) | ~ (plus_plus_real(v2) = % 236.94/36.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 236.94/36.92 (power_power_real(v2) = v1) | ~ (power_power_real(v2) = v0)) & ! [v0: $i] % 236.94/36.92 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit1(v2) = v1) | ~ (bit1(v2) = % 236.94/36.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit0(v2) = % 236.94/36.92 v1) | ~ (bit0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 236.94/36.92 = v0 | ~ (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) = % 236.94/36.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 236.94/36.92 (power_power_int(v2) = v1) | ~ (power_power_int(v2) = v0)) & ! [v0: $i] : % 236.94/36.92 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (plus_plus_int(v2) = v1) | ~ % 236.94/36.92 (plus_plus_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 236.94/36.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ % 236.94/36.92 (hBOOL(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 236.94/36.92 : ! [v2: $i] : (v1 = v0 | ~ (is_bool(v2) = v1) | ~ (is_bool(v2) = v0)) & ? % 236.94/36.92 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (times_times_int(v1, v0) = v2 & $i(v2)) % 236.94/36.92 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (if_nat(v1, v0) = v2 & $i(v2)) & % 236.94/36.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_r1134773055l_bool(v1, v0) = v2 % 236.94/36.92 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 236.94/36.92 (hAPP_n1699378549t_bool(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : % 236.94/36.92 ? [v2: $i] : (hAPP_nat_nat(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] % 236.94/36.92 : ? [v2: $i] : (hAPP_nat_real(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 236.94/36.92 $i] : ? [v2: $i] : (hAPP_real_real(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : % 236.94/36.92 ? [v1: $i] : ? [v2: $i] : (hAPP_i1948725293t_bool(v1, v0) = v2 & $i(v2)) & ? % 236.94/36.92 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_nat_int(v1, v0) = v2 & $i(v2)) & % 236.94/36.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_int_int(v1, v0) = v2 & $i(v2)) % 236.94/36.92 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_real_bool(v1, v0) = v2 & % 236.94/36.92 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_nat_bool(v1, v0) = % 236.94/36.92 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_int_bool(v1, % 236.94/36.92 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] : (hBOOL(v0) % 236.94/36.92 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (is_bool(v0) = v1) & ? % 236.94/36.92 [v0: $i] : ? [v1: $i] : (sqrt(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] % 236.94/36.92 : (succ(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (plus_plus_nat(v0) = % 236.94/36.92 v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (number267125858f_real(v0) = v1 & % 236.94/36.92 $i(v1)) & ? [v0: $i] : ? [v1: $i] : (number_number_of_int(v0) = v1 & % 236.94/36.92 $i(v1)) & ? [v0: $i] : ? [v1: $i] : (power_power_nat(v0) = v1 & $i(v1)) & % 236.94/36.92 ? [v0: $i] : ? [v1: $i] : (plus_plus_real(v0) = v1 & $i(v1)) & ? [v0: $i] : % 236.94/36.92 ? [v1: $i] : (power_power_real(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] % 236.94/36.92 : (bit1(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (bit0(v0) = v1 & % 236.94/36.92 $i(v1)) & ? [v0: $i] : ? [v1: $i] : (number_number_of_nat(v0) = v1 & % 236.94/36.92 $i(v1)) & ? [v0: $i] : ? [v1: $i] : (power_power_int(v0) = v1 & $i(v1)) & % 236.94/36.92 ? [v0: $i] : ? [v1: $i] : (plus_plus_int(v0) = v1 & $i(v1)) % 236.94/36.92 % 236.94/36.92 Further assumptions not needed in the proof: % 236.94/36.92 -------------------------------------------- % 236.94/36.92 fact_100_add__Pls__right, fact_101_add__Pls, fact_102_add__Bit0__Bit0, % 236.94/36.92 fact_103_Bit0__def, fact_104_zadd__0__right, fact_105_zadd__0, % 236.94/36.92 fact_107_semiring__numeral__0__eq__0, fact_108_semiring__numeral__0__eq__0, % 236.94/36.92 fact_110_number__of__Pls, fact_112_semiring__norm_I112_J, % 236.94/36.92 fact_114_add__numeral__0, fact_116_add__numeral__0__right, % 236.94/36.92 fact_118_power__eq__0__iff__number__of, fact_119_power__eq__0__iff__number__of, % 236.94/36.92 fact_120_add__number__of__left, fact_121_add__number__of__left, % 236.94/36.92 fact_122_add__number__of__eq, fact_123_add__number__of__eq, % 236.94/36.92 fact_124_number__of__add, fact_125_number__of__add, fact_126_add__Bit1__Bit0, % 236.94/36.92 fact_127_add__Bit0__Bit1, fact_130_number__of__int, fact_132_number__of__int, % 236.94/36.92 fact_141_number__of__Bit0, fact_142_number__of__Bit0, fact_144_number__of__Bit1, % 236.94/36.92 fact_155_of__nat__0__less__iff, fact_156_of__nat__0__less__iff, % 236.94/36.92 fact_157_one__less__power, fact_158_one__less__power, fact_159_one__less__power, % 236.94/36.92 fact_160_power__0__left, fact_161_power__0__left, fact_162_power__0__left, % 236.94/36.92 fact_164_power__strict__decreasing, fact_165_power__strict__decreasing, % 236.94/36.92 fact_168_zero__less__two, fact_169_int__gr__induct, fact_170_tn0, % 236.94/36.92 fact_171_less__zeroE, fact_172_real__zero__not__eq__one, % 236.94/36.92 fact_173_less__not__refl, fact_174_not__add__less1, fact_175_not__add__less2, % 236.94/36.92 fact_176_number__of__is__id, fact_177_nat__neq__iff, fact_178_nat__add__commute, % 236.94/36.92 fact_179_nat__add__left__commute, fact_180_nat__add__assoc, % 236.94/36.92 fact_181_nat__add__left__cancel, fact_182_nat__add__right__cancel, % 236.94/36.92 fact_183_nat__add__left__cancel__less, fact_184_linorder__neqE__nat, % 236.94/36.92 fact_185_less__irrefl__nat, fact_186_less__not__refl2, % 236.94/36.92 fact_187_less__not__refl3, fact_188_trans__less__add1, % 236.94/36.92 fact_189_trans__less__add2, fact_190_add__less__mono1, fact_191_add__less__mono, % 236.94/36.92 fact_192_less__add__eq__less, fact_193_add__lessD1, fact_194_nat__less__cases, % 236.94/36.92 fact_195_gr0I, fact_196_gr__implies__not0, fact_197_nat__power__less__imp__less, % 236.94/36.92 fact_198_less__nat__zero__code, fact_199_nat__zero__less__power__iff, fact_1_t1, % 236.94/36.92 fact_200_add__gr__0, fact_201_neq0__conv, fact_202_not__less0, % 236.94/36.92 fact_203_zero__less__power__nat__eq, % 236.94/36.92 fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J, % 236.94/36.92 fact_205_zero__less__power__nat__eq__number__of, fact_206_zless__int, % 236.94/36.92 fact_208_linorder__neqE__linordered__idom, % 236.94/36.92 fact_209_linorder__neqE__linordered__idom, fact_210_add__eq__self__zero, % 236.94/36.92 fact_211_add__is__0, fact_212_Nat_Oadd__0__right, fact_213_plus__nat_Oadd__0, % 236.94/36.92 fact_214_power__one__right, fact_215_power__one__right, % 236.94/36.92 fact_216_power__one__right, fact_217_of__nat__eq__iff, % 236.94/36.92 fact_218_of__nat__eq__iff, fact_219_of__nat__eq__iff, % 236.94/36.92 fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J, % 236.94/36.92 fact_221_int__if__cong, fact_224_one__neq__zero, fact_225_one__neq__zero, % 236.94/36.92 fact_226_one__neq__zero, fact_227_zero__neq__one, fact_228_zero__neq__one, % 236.94/36.92 fact_229_zero__neq__one, fact_22_power__0__left__number__of, % 236.94/36.92 fact_230_field__power__not__zero, fact_231_field__power__not__zero, % 236.94/36.92 fact_232_power__one, fact_233_power__one, fact_234_power__one, % 236.94/36.92 fact_235_of__nat__less__iff, fact_236_of__nat__less__iff, % 236.94/36.92 fact_237_of__nat__less__iff, fact_238_less__imp__of__nat__less, % 236.94/36.92 fact_239_less__imp__of__nat__less, fact_23_power__0__left__number__of, % 236.94/36.92 fact_240_less__imp__of__nat__less, fact_241_of__nat__less__imp__less, % 236.94/36.92 fact_242_of__nat__less__imp__less, fact_243_of__nat__less__imp__less, % 236.94/36.92 fact_244_of__nat__add, fact_245_of__nat__add, fact_246_of__nat__add, % 236.94/36.92 fact_247_of__nat__1, fact_248_of__nat__1, fact_24_power__0__left__number__of, % 236.94/36.92 fact_250_of__nat__power, fact_251_of__nat__power, fact_252_of__nat__power, % 236.94/36.92 fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J, % 236.94/36.92 fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J, % 236.94/36.92 fact_256_pos__add__strict, fact_257_pos__add__strict, % 236.94/36.92 fact_259_not__one__less__zero, fact_260_not__one__less__zero, % 236.94/36.92 fact_261_not__one__less__zero, fact_262_zero__less__one, % 236.94/36.92 fact_263_zero__less__one, fact_265_zero__less__power, % 236.94/36.92 fact_266_zero__less__power, fact_268_less__add__one, fact_269_less__add__one, % 236.94/36.92 fact_270_less__add__one, fact_271_power__inject__exp, % 236.94/36.92 fact_272_power__inject__exp, fact_273_power__inject__exp, % 236.94/36.92 fact_274_power__strict__increasing__iff, % 236.94/36.92 fact_275_power__strict__increasing__iff, % 236.94/36.92 fact_276_power__strict__increasing__iff, fact_277_power__less__imp__less__exp, % 236.94/36.92 fact_278_power__less__imp__less__exp, fact_279_power__less__imp__less__exp, % 236.94/36.92 fact_280_power__strict__increasing, fact_281_power__strict__increasing, % 236.94/36.92 fact_282_power__strict__increasing, fact_283_power__eq__0__iff, % 236.94/36.92 fact_284_power__eq__0__iff, fact_285_power__eq__0__iff, % 236.94/36.92 fact_286_of__nat__less__0__iff, fact_287_of__nat__less__0__iff, % 236.94/36.92 fact_288_of__nat__less__0__iff, fact_289_power__0, fact_290_power__0, % 236.94/36.92 fact_291_power__0, fact_292_of__nat__0, fact_293_of__nat__0, % 236.94/36.92 fact_294_of__nat__0, fact_295_transfer__int__nat__numerals_I1_J, % 236.94/36.92 fact_298_less__imp__add__positive, fact_299_exp__eq__1, fact_29_n0, % 236.94/36.92 fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, % 236.94/36.92 fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, % 236.94/36.92 fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, % 236.94/36.92 fact_303_zero__less__double__add__iff__zero__less__single__add, % 236.94/36.92 fact_305_double__add__less__zero__iff__single__add__less__zero, % 236.94/36.92 fact_306_double__add__less__zero__iff__single__add__less__zero, % 236.94/36.92 fact_307_zero__reorient, fact_308_zero__reorient, fact_309_zero__reorient, % 236.94/36.92 fact_30_zless__linear, fact_310_add__right__imp__eq, % 236.94/36.92 fact_311_add__right__imp__eq, fact_312_add__right__imp__eq, % 236.94/36.92 fact_313_add__imp__eq, fact_314_add__imp__eq, fact_315_add__imp__eq, % 236.94/36.92 fact_316_add__left__imp__eq, fact_317_add__left__imp__eq, % 236.94/36.92 fact_318_add__left__imp__eq, % 236.94/36.92 fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 236.94/36.92 fact_31_less__number__of__int__code, % 236.94/36.92 fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 236.94/36.92 fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, % 236.94/36.92 fact_322_add__right__cancel, fact_323_add__right__cancel, % 236.94/36.92 fact_324_add__right__cancel, fact_325_add__left__cancel, % 236.94/36.92 fact_326_add__left__cancel, fact_327_add__left__cancel, % 236.94/36.92 fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 236.94/36.92 fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 236.94/36.92 fact_32_plus__numeral__code_I9_J, % 236.94/36.92 fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, % 236.94/36.92 fact_331_ab__semigroup__add__class_Oadd__ac_I1_J, % 236.94/36.92 fact_332_ab__semigroup__add__class_Oadd__ac_I1_J, % 236.94/36.92 fact_333_ab__semigroup__add__class_Oadd__ac_I1_J, % 236.94/36.92 fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 236.94/36.92 fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 236.94/36.92 fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, % 236.94/36.92 fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 236.94/36.92 fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 236.94/36.92 fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, % 236.94/36.92 fact_33_less__number__of, % 236.94/36.92 fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 236.94/36.92 fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 236.94/36.92 fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, % 236.94/36.92 fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 236.94/36.92 fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 236.94/36.92 fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, % 236.94/36.92 fact_346_one__reorient, fact_347_one__reorient, fact_348_one__reorient, % 236.94/36.92 fact_349_add__0__iff, fact_34_less__number__of, fact_350_add__0__iff, % 236.94/36.92 fact_351_add__0__iff, fact_352_add_Ocomm__neutral, fact_353_add_Ocomm__neutral, % 236.94/36.92 fact_354_add_Ocomm__neutral, % 236.94/36.92 fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 236.94/36.92 fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 236.94/36.92 fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, % 236.94/36.92 fact_358_add__0__right, fact_359_add__0__right, fact_360_add__0__right, % 236.94/36.92 fact_361_double__zero__sym, fact_362_double__zero__sym, fact_363_add__0, % 236.94/36.92 fact_364_add__0, fact_365_add__0, % 236.94/36.92 fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 236.94/36.92 fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 236.94/36.92 fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, % 236.94/36.92 fact_369_add__0__left, fact_36_zpower__int, fact_370_add__0__left, % 236.94/36.92 fact_371_add__0__left, fact_372_add__less__imp__less__left, % 236.94/36.92 fact_373_add__less__imp__less__left, fact_374_add__less__imp__less__left, % 236.94/36.92 fact_375_add__less__imp__less__right, fact_376_add__less__imp__less__right, % 236.94/36.92 fact_377_add__less__imp__less__right, fact_378_add__strict__mono, % 236.94/36.92 fact_379_add__strict__mono, fact_37_int__power, fact_380_add__strict__mono, % 236.94/36.92 fact_381_add__strict__left__mono, fact_382_add__strict__left__mono, % 236.94/36.92 fact_383_add__strict__left__mono, fact_384_add__strict__right__mono, % 236.94/36.92 fact_385_add__strict__right__mono, fact_386_add__strict__right__mono, % 236.94/36.92 fact_387_add__less__cancel__left, fact_388_add__less__cancel__left, % 236.94/36.92 fact_389_add__less__cancel__left, fact_38_zadd__int__left, % 236.94/36.92 fact_390_add__less__cancel__right, fact_391_add__less__cancel__right, % 236.94/36.92 fact_392_add__less__cancel__right, % 236.94/36.92 fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, % 236.94/36.92 fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, % 236.94/36.92 fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, % 236.94/36.92 fact_396_nat__power__eq__0__iff, fact_397_add__neg__neg, fact_398_add__neg__neg, % 236.94/36.92 fact_399_add__neg__neg, fact_39_zadd__int, fact_400_add__pos__pos, % 236.94/36.92 fact_401_add__pos__pos, fact_403_realpow__pos__nth__unique, % 236.94/36.92 fact_404_realpow__pos__nth, fact_405_tpos, fact_406_nat__number__of__add__1, % 236.94/36.92 fact_408_add__le__cancel__right, fact_409_add__le__cancel__right, % 236.94/36.92 fact_410_add__le__cancel__right, fact_411_add__le__cancel__left, % 236.94/36.92 fact_412_add__le__cancel__left, fact_413_add__le__cancel__left, % 236.94/36.92 fact_414_add__right__mono, fact_415_add__right__mono, fact_416_add__right__mono, % 236.94/36.92 fact_417_add__left__mono, fact_418_add__left__mono, fact_419_add__left__mono, % 236.94/36.92 fact_41_nat__number__of__Pls, fact_420_add__mono, fact_421_add__mono, % 236.94/36.92 fact_422_add__mono, fact_423_add__le__imp__le__right, % 236.94/36.92 fact_424_add__le__imp__le__right, fact_425_add__le__imp__le__right, % 236.94/36.92 fact_426_add__le__imp__le__left, fact_427_add__le__imp__le__left, % 236.94/36.92 fact_428_add__le__imp__le__left, fact_429_power__increasing, % 236.94/36.92 fact_42_semiring__norm_I113_J, fact_430_power__increasing, % 236.94/36.92 fact_431_power__increasing, fact_432_less__eq__int__code_I16_J, % 236.94/36.92 fact_433_rel__simps_I34_J, fact_434_rel__simps_I19_J, % 236.94/36.92 fact_435_less__eq__int__code_I13_J, fact_436_rel__simps_I31_J, % 236.94/36.92 fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, % 236.94/36.92 fact_438_zle__refl, fact_439_zle__linear, fact_43_int__eq__0__conv, % 236.94/36.92 fact_440_zle__trans, fact_441_zle__antisym, fact_442_le__number__of, % 236.94/36.92 fact_443_le__number__of, fact_444_of__nat__le__iff, fact_445_of__nat__le__iff, % 236.94/36.92 fact_446_of__nat__le__iff, fact_448_zadd__left__mono, % 236.94/36.92 fact_449_less__eq__number__of__int__code, fact_44_int__0, % 236.94/36.92 fact_450_le__special_I1_J, fact_451_le__special_I1_J, fact_452_le__special_I3_J, % 236.94/36.92 fact_453_le__special_I3_J, fact_454_power__decreasing, % 236.94/36.92 fact_455_power__decreasing, fact_456_power__decreasing, % 236.94/36.92 fact_457_power__increasing__iff, fact_458_power__increasing__iff, % 236.94/36.92 fact_459_power__increasing__iff, fact_460_power__le__imp__le__exp, % 236.94/36.92 fact_461_power__le__imp__le__exp, fact_462_power__le__imp__le__exp, % 236.94/36.92 fact_467_zero__le__double__add__iff__zero__le__single__add, % 236.94/36.92 fact_468_zero__le__double__add__iff__zero__le__single__add, % 236.94/36.92 fact_469_double__add__le__zero__iff__single__add__le__zero, % 236.94/36.92 fact_46_less__int__code_I16_J, % 236.94/36.92 fact_470_double__add__le__zero__iff__single__add__le__zero, % 236.94/36.92 fact_471_add__nonneg__nonneg, fact_472_add__nonneg__nonneg, % 236.94/36.92 fact_473_add__nonneg__nonneg, fact_474_add__nonneg__eq__0__iff, % 236.94/36.92 fact_475_add__nonneg__eq__0__iff, fact_476_add__nonneg__eq__0__iff, % 236.94/36.92 fact_477_add__increasing, fact_478_add__increasing, fact_479_add__increasing, % 236.94/36.92 fact_47_rel__simps_I17_J, fact_480_add__increasing2, fact_481_add__increasing2, % 236.94/36.92 fact_482_add__increasing2, fact_483_add__nonpos__nonpos, % 236.94/36.92 fact_484_add__nonpos__nonpos, fact_485_add__nonpos__nonpos, % 236.94/36.92 fact_486_add__less__le__mono, fact_487_add__less__le__mono, % 236.94/36.92 fact_488_add__less__le__mono, fact_489_add__le__less__mono, % 236.94/36.92 fact_490_add__le__less__mono, fact_491_add__le__less__mono, % 236.94/36.92 fact_492_not__one__le__zero, fact_493_not__one__le__zero, % 236.94/36.92 fact_494_not__one__le__zero, fact_495_zero__le__one, fact_496_zero__le__one, % 236.94/36.92 fact_497_zero__le__one, fact_498_le__number__of__eq__not__less, % 236.94/36.92 fact_499_le__number__of__eq__not__less, fact_49_less__int__code_I13_J, % 236.94/36.92 fact_500_le__number__of__eq__not__less, fact_501_zero__le__power, % 236.94/36.92 fact_502_zero__le__power, fact_503_zero__le__power, fact_504_power__mono, % 236.94/36.92 fact_505_power__mono, fact_506_power__mono, fact_507_one__le__power, % 236.94/36.92 fact_508_one__le__power, fact_509_one__le__power, fact_50_rel__simps_I14_J, % 236.94/36.92 fact_510_zero__le__imp__of__nat, fact_511_zero__le__imp__of__nat, % 236.94/36.92 fact_512_zero__le__imp__of__nat, fact_513_of__nat__0__le__iff, % 236.94/36.92 fact_514_of__nat__0__le__iff, fact_515_of__nat__0__le__iff, % 236.94/36.92 fact_516_rel__simps_I22_J, fact_517_rel__simps_I32_J, % 236.94/36.92 fact_518_less__eq__int__code_I14_J, fact_519_rel__simps_I21_J, % 236.94/36.92 fact_51_zadd__strict__right__mono, fact_520_rel__simps_I27_J, % 236.94/36.92 fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, % 236.94/36.92 fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, % 236.94/36.92 fact_523_zadd__zless__mono, % 236.94/36.92 fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, % 236.94/36.92 fact_525_transfer__int__nat__quantifiers_I2_J, % 236.94/36.92 fact_526_transfer__int__nat__quantifiers_I1_J, fact_527_zero__zle__int, % 236.94/36.92 fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, % 236.94/36.92 fact_529_zle__iff__zadd, fact_52_add__nat__number__of, % 236.94/36.92 fact_530_semiring__1__add__number__of, fact_533_semiring__number__of__add__1, % 236.94/36.92 fact_534_semiring__number__of__add__1, fact_535_semiring__number__of__add__1, % 236.94/36.92 fact_536_add__pos__nonneg, fact_537_add__pos__nonneg, fact_539_add__nonneg__pos, % 236.94/36.92 fact_540_add__nonneg__pos, fact_542_add__strict__increasing, % 236.94/36.92 fact_543_add__strict__increasing, fact_545_add__strict__increasing2, % 236.94/36.92 fact_546_add__strict__increasing2, fact_548_add__neg__nonpos, % 236.94/36.92 fact_549_add__neg__nonpos, fact_550_add__neg__nonpos, fact_551_add__nonpos__neg, % 236.94/36.92 fact_552_add__nonpos__neg, fact_553_add__nonpos__neg, % 236.94/36.92 fact_554_power__less__imp__less__base, fact_555_power__less__imp__less__base, % 236.94/36.92 fact_556_power__less__imp__less__base, fact_557_eq__0__number__of, % 236.94/36.92 fact_558_eq__number__of__0, fact_560_rel__simps_I29_J, % 236.94/36.92 fact_561_rel__simps_I15_J, fact_562_less__int__code_I14_J, % 236.94/36.92 fact_563_rel__simps_I33_J, fact_564_less__eq__int__code_I15_J, % 236.94/36.92 fact_566_int__le__0__conv, fact_568_succ__Bit0, fact_569_succ__Bit1, % 236.94/36.92 fact_56_eq__number__of, fact_570_zle__add1__eq__le, fact_571_add1__zle__eq, % 236.94/36.92 fact_572_zless__imp__add1__zle, fact_573_succ__def, % 236.94/36.92 fact_574_power__eq__imp__eq__base, fact_575_power__eq__imp__eq__base, % 236.94/36.92 fact_576_power__eq__imp__eq__base, fact_577_semiring__add__number__of, % 236.94/36.92 fact_578_semiring__add__number__of, fact_579_semiring__add__number__of, % 236.94/36.92 fact_57_eq__number__of, fact_582_number__of__succ, fact_584_add__Bit1__Bit1, % 236.94/36.92 fact_585_power__strict__mono, fact_586_power__strict__mono, % 236.94/36.92 fact_587_power__strict__mono, fact_58_number__of__reorient, % 236.94/36.92 fact_598_of__nat__number__of__lemma, fact_599_of__nat__number__of__lemma, % 236.94/36.92 fact_59_number__of__reorient, fact_608_number__of1, % 236.94/36.92 fact_60_number__of__reorient, fact_610_zero__le__imp__eq__int, % 236.94/36.92 fact_611_nonneg__int__cases, fact_612_le0, fact_613_less__eq__nat_Osimps_I1_J, % 236.94/36.92 fact_614_le__0__eq, fact_615_less__or__eq__imp__le, % 236.94/36.92 fact_616_le__neq__implies__less, fact_617_less__imp__le__nat, % 236.94/36.92 fact_618_le__eq__less__or__eq, fact_619_nat__less__le, fact_61_rel__simps_I51_J, % 236.94/36.92 fact_620_le__refl, fact_621_nat__le__linear, fact_622_eq__imp__le, % 236.94/36.92 fact_623_le__trans, fact_624_le__antisym, fact_625_less__eq__real__def, % 236.94/36.92 fact_626_real__less__def, fact_627_le__add2, fact_628_le__add1, % 236.94/36.92 fact_629_le__iff__add, fact_62_rel__simps_I48_J, % 236.94/36.92 fact_630_nat__add__left__cancel__le, fact_631_trans__le__add1, % 236.94/36.92 fact_632_trans__le__add2, fact_633_add__le__mono1, fact_634_add__le__mono, % 236.94/36.92 fact_635_add__leD2, fact_636_add__leD1, fact_637_add__leE, % 236.94/36.92 fact_638_real__add__left__mono, % 236.94/36.92 fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J, % 236.94/36.92 fact_63_even__less__0__iff, fact_640_zle__int, fact_641_le__nat__number__of, % 236.94/36.92 fact_643_conj__le__cong, fact_644_imp__le__cong, fact_646_nonneg__eq__int, % 236.94/36.92 fact_647_mono__nat__linear__lb, fact_648_real__le__refl, % 236.94/36.92 fact_649_real__le__linear, fact_64_even__less__0__iff, fact_650_real__le__trans, % 236.94/36.92 fact_651_real__le__antisym, fact_652_int__ge__induct, % 236.94/36.92 fact_653_ex__least__nat__le, fact_654_less__mono__imp__le__mono, % 236.94/36.92 fact_655_order__refl, fact_656_order__refl, fact_657_order__refl, % 236.94/36.92 fact_658_linorder__le__cases, fact_659_linorder__le__cases, fact_65_zadd__assoc, % 236.94/36.92 fact_660_linorder__le__cases, fact_661_xt1_I6_J, fact_662_xt1_I6_J, % 236.94/36.92 fact_663_xt1_I6_J, fact_664_xt1_I5_J, fact_665_xt1_I5_J, fact_666_xt1_I5_J, % 236.94/36.92 fact_667_order__trans, fact_668_order__trans, fact_669_order__trans, % 236.94/36.92 fact_66_zadd__left__commute, fact_670_order__antisym, fact_671_order__antisym, % 236.94/36.92 fact_672_order__antisym, fact_673_xt1_I4_J, fact_674_xt1_I4_J, % 236.94/36.92 fact_675_xt1_I4_J, fact_676_ord__le__eq__trans, fact_677_ord__le__eq__trans, % 236.94/36.92 fact_678_ord__le__eq__trans, fact_679_xt1_I3_J, fact_67_zadd__commute, % 236.94/36.92 fact_680_xt1_I3_J, fact_681_xt1_I3_J, fact_682_ord__eq__le__trans, % 236.94/36.92 fact_683_ord__eq__le__trans, fact_684_ord__eq__le__trans, % 236.94/36.92 fact_685_order__antisym__conv, fact_686_order__antisym__conv, % 236.94/36.92 fact_687_order__antisym__conv, fact_688_order__eq__refl, % 236.94/36.92 fact_689_real__lbound__gt__zero, fact_68_int__int__eq, fact_692_mult__Bit1, % 236.94/36.92 fact_693_real__sqrt__gt__zero, fact_694_real__sqrt__not__eq__zero, % 236.94/36.92 fact_695_real__sqrt__lt__0__iff, fact_696_real__sqrt__gt__0__iff, % 236.94/36.92 fact_697_real__sqrt__lt__1__iff, fact_698_real__sqrt__gt__1__iff, % 236.94/36.92 fact_69_less__special_I3_J, fact_70_less__special_I3_J, % 236.94/36.92 fact_73_rel__simps_I12_J, fact_74_less__int__code_I15_J, % 236.94/36.92 fact_75_rel__simps_I16_J, fact_76_rel__simps_I10_J, % 236.94/36.92 fact_78_bin__less__0__simps_I4_J, fact_80_bin__less__0__simps_I3_J, % 236.94/36.92 fact_82_zless__add1__eq, fact_83_int__less__0__conv, fact_89_double__eq__0__iff, % 236.94/36.92 fact_90_double__eq__0__iff, fact_91_rel__simps_I46_J, fact_92_rel__simps_I39_J, % 236.94/36.92 fact_93_rel__simps_I50_J, fact_94_rel__simps_I49_J, fact_95_rel__simps_I44_J, % 236.94/36.92 fact_96_rel__simps_I38_J, fact_97_Bit0__Pls, fact_99_int__0__neq__1, % 236.94/36.92 gsy_c_fFalse, gsy_c_fTrue, gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool, % 236.94/36.92 gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool, % 236.94/36.92 gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool, % 236.94/36.92 help_If_1_1_If_000tc__Nat__Onat_T, help_If_2_1_If_000tc__Nat__Onat_T, % 236.94/36.92 help_If_3_1_If_000tc__Nat__Onat_T % 236.94/36.92 % 236.94/36.92 Those formulas are unsatisfiable: % 236.94/36.92 --------------------------------- % 236.94/36.92 % 236.94/36.92 Begin of proof % 236.94/36.92 | % 236.94/36.93 | ALPHA: (fact_0_n1pos) implies: % 236.94/36.93 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 236.94/36.93 | (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & % 236.94/36.93 | plus_plus_int(one_one_int) = v1 & % 236.94/36.93 | hAPP_nat_int(semiri1621563631at_int, n) = v2 & hAPP_int_int(v1, v2) = % 236.94/36.93 | v3 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & % 236.94/36.93 | $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_2_sum__power2__eq__zero__iff) implies: % 236.94/36.93 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 236.94/36.93 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 236.94/36.93 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 236.94/36.93 | [v8: $i] : ! [v9: $i] : ( ~ (power_power_int(v4) = v8) | ~ % 236.94/36.93 | (power_power_int(v3) = v5) | ~ (plus_plus_int(v6) = v7) | ~ % 236.94/36.93 | (hAPP_nat_int(v8, v2) = v9) | ~ (hAPP_nat_int(v5, v2) = v6) | ~ % 236.94/36.93 | (hAPP_int_int(v7, v9) = zero_zero_int) | ~ $i(v4) | ~ $i(v3) | % 236.94/36.93 | (v4 = zero_zero_int & v3 = zero_zero_int)) & ! [v3: $i] : ! [v4: % 236.94/36.93 | $i] : ! [v5: $i] : ! [v6: $i] : (v6 = zero_zero_int | ~ % 236.94/36.93 | (power_power_int(zero_zero_int) = v3) | ~ (plus_plus_int(v4) = v5) % 236.94/36.93 | | ~ (hAPP_nat_int(v3, v2) = v4) | ~ (hAPP_int_int(v5, v4) = v6))) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_4_one__power2) implies: % 236.94/36.93 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 % 236.94/36.93 | & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 236.94/36.93 | power_power_int(one_one_int) = v0 & hAPP_nat_int(v0, v3) = % 236.94/36.93 | one_one_int & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_5_one__power2) implies: % 236.94/36.93 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.93 | (power_power_nat(one_one_nat) = v0 & hAPP_nat_nat(v0, v3) = one_one_nat % 236.94/36.93 | & bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 236.94/36.93 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_6_one__power2) implies: % 236.94/36.93 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.93 | (power_power_real(one_one_real) = v0 & hAPP_nat_real(v0, v3) = % 236.94/36.93 | one_one_real & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.93 | number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_7_zero__power2) implies: % 236.94/36.93 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = v1 % 236.94/36.93 | & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 236.94/36.93 | power_power_int(zero_zero_int) = v0 & hAPP_nat_int(v0, v3) = % 236.94/36.93 | zero_zero_int & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_8_zero__power2) implies: % 236.94/36.93 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.93 | (power_power_nat(zero_zero_nat) = v0 & hAPP_nat_nat(v0, v3) = % 236.94/36.93 | zero_zero_nat & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.93 | number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_9_zero__power2) implies: % 236.94/36.93 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 236.94/36.93 | (power_power_real(zero_zero_real) = v0 & hAPP_nat_real(v0, v3) = % 236.94/36.93 | zero_zero_real & bit1(pls) = v1 & bit0(v1) = v2 & % 236.94/36.93 | number_number_of_nat(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_10_zero__eq__power2) implies: % 236.94/36.93 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 236.94/36.93 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 236.94/36.93 | [v3: $i] : ! [v4: $i] : (v3 = zero_zero_int | ~ % 236.94/36.93 | (power_power_int(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = % 236.94/36.93 | zero_zero_int) & hAPP_nat_int(v4, v2) = v5 & $i(v5))) & ! [v3: % 236.94/36.93 | $i] : ( ~ (power_power_int(zero_zero_int) = v3) | hAPP_nat_int(v3, % 236.94/36.93 | v2) = zero_zero_int)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_11_zero__eq__power2) implies: % 236.94/36.93 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 236.94/36.93 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 236.94/36.93 | [v3: $i] : ! [v4: $i] : (v3 = zero_zero_real | ~ % 236.94/36.93 | (power_power_real(v3) = v4) | ~ $i(v3) | ? [v5: $i] : ( ~ (v5 = % 236.94/36.93 | zero_zero_real) & hAPP_nat_real(v4, v2) = v5 & $i(v5))) & ! % 236.94/36.93 | [v3: $i] : ( ~ (power_power_real(zero_zero_real) = v3) | % 236.94/36.93 | hAPP_nat_real(v3, v2) = zero_zero_real)) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_12_add__special_I2_J) implies: % 236.94/36.93 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v1 & % 236.94/36.93 | plus_plus_int(v1) = v2 & plus_plus_int(one_one_int) = v0 & $i(v2) & % 236.94/36.93 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_int(v2, % 236.94/36.93 | v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : % 236.94/36.93 | (number_number_of_int(v4) = v6 & number_number_of_int(v3) = v5 & % 236.94/36.93 | hAPP_int_int(v0, v5) = v6 & $i(v6) & $i(v5)))) % 236.94/36.93 | % 236.94/36.93 | ALPHA: (fact_13_add__special_I2_J) implies: % 237.20/36.93 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 237.20/36.93 | (plus_plus_real(one_one_real) = v0 & bit1(pls) = v1 & % 237.20/36.93 | plus_plus_int(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 237.20/36.93 | [v4: $i] : ( ~ (hAPP_int_int(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] % 237.20/36.93 | : ? [v6: $i] : (number267125858f_real(v4) = v6 & % 237.20/36.93 | number267125858f_real(v3) = v5 & hAPP_real_real(v0, v5) = v6 & % 237.20/36.93 | $i(v6) & $i(v5)))) % 237.20/36.93 | % 237.20/36.93 | ALPHA: (fact_14_add__special_I3_J) implies: % 237.20/36.93 | (13) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.20/36.93 | ~ (number_number_of_int(v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? % 237.20/36.93 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (number_number_of_int(v6) = % 237.20/36.93 | v4 & plus_plus_int(v2) = v3 & plus_plus_int(v1) = v5 & % 237.20/36.93 | hAPP_int_int(v5, v0) = v6 & hAPP_int_int(v3, one_one_int) = v4 & % 237.20/36.93 | $i(v6) & $i(v5) & $i(v4) & $i(v3)))) % 237.20/36.93 | % 237.20/36.93 | ALPHA: (fact_15_add__special_I3_J) implies: % 237.20/36.94 | (14) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.20/36.94 | ~ (number267125858f_real(v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? % 237.20/36.94 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (number267125858f_real(v6) % 237.20/36.94 | = v4 & plus_plus_real(v2) = v3 & hAPP_real_real(v3, % 237.20/36.94 | one_one_real) = v4 & plus_plus_int(v1) = v5 & hAPP_int_int(v5, % 237.20/36.94 | v0) = v6 & $i(v6) & $i(v5) & $i(v4) & $i(v3)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_18_semiring__one__add__one__is__two) implies: % 237.20/36.94 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.20/36.94 | (number_number_of_int(v3) = v1 & bit1(pls) = v2 & bit0(v2) = v3 & % 237.20/36.94 | plus_plus_int(one_one_int) = v0 & hAPP_int_int(v0, one_one_int) = v1 % 237.20/36.94 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_20_semiring__one__add__one__is__two) implies: % 237.20/36.94 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.20/36.94 | (number267125858f_real(v3) = v1 & plus_plus_real(one_one_real) = v0 & % 237.20/36.94 | hAPP_real_real(v0, one_one_real) = v1 & bit1(pls) = v2 & bit0(v2) = % 237.20/36.94 | v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_21_quartic__square__square) implies: % 237.20/36.94 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.20/36.94 | (bit1(pls) = v0 & bit0(v1) = v3 & bit0(v0) = v1 & % 237.20/36.94 | number_number_of_nat(v3) = v4 & number_number_of_nat(v1) = v2 & % 237.20/36.94 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: % 237.20/36.94 | $i] : ( ~ (power_power_int(v5) = v6) | ~ $i(v5) | ? [v7: $i] : % 237.20/36.94 | ? [v8: $i] : ? [v9: $i] : (power_power_int(v7) = v8 & % 237.20/36.94 | hAPP_nat_int(v8, v2) = v9 & hAPP_nat_int(v6, v4) = v9 & % 237.20/36.94 | hAPP_nat_int(v6, v2) = v7 & $i(v9) & $i(v8) & $i(v7)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_45_nat__1__add__1) implies: % 237.20/36.94 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.20/36.94 | (plus_plus_nat(one_one_nat) = v0 & hAPP_nat_nat(v0, one_one_nat) = v1 % 237.20/36.94 | & bit1(pls) = v2 & bit0(v2) = v3 & number_number_of_nat(v3) = v1 & % 237.20/36.94 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_48_rel__simps_I2_J) implies: % 237.20/36.94 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 237.20/36.94 | hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & hBOOL(v1) = v2 & % 237.20/36.94 | hAPP_int_bool(v0, pls) = v1 & $i(v1) & $i(v0)) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_71_less__special_I1_J) implies: % 237.20/36.94 | (20) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int, pls) % 237.20/36.94 | = v1 & hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & % 237.20/36.94 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, % 237.20/36.94 | v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: % 237.20/36.94 | $i] : ? [v7: any] : (number_number_of_int(v2) = v5 & hBOOL(v6) % 237.20/36.94 | = v7 & hBOOL(v3) = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & % 237.20/36.94 | $i(v5) & ( ~ (v4 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : % 237.20/36.94 | ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: % 237.20/36.94 | $i] : ? [v6: any] : ? [v7: any] : (number_number_of_int(v2) = % 237.20/36.94 | v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & hAPP_int_bool(v0, v4) = % 237.20/36.94 | v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_72_less__special_I1_J) implies: % 237.20/36.94 | (21) ? [v0: $i] : ? [v1: $i] : (hAPP_r1134773055l_bool(ord_less_real, % 237.20/36.94 | zero_zero_real) = v0 & hAPP_i1948725293t_bool(ord_less_int, pls) = % 237.20/36.94 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 237.20/36.94 | (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 237.20/36.94 | $i] : ? [v6: $i] : ? [v7: any] : (number267125858f_real(v2) = % 237.20/36.94 | v5 & hBOOL(v6) = v7 & hBOOL(v3) = v4 & hAPP_real_bool(v0, v5) = % 237.20/36.94 | v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = 0))) & ! [v2: $i] : % 237.20/36.94 | ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: % 237.20/36.94 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 237.20/36.94 | (number267125858f_real(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 % 237.20/36.94 | & hAPP_real_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | % 237.20/36.94 | v7 = 0)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_77_rel__simps_I4_J) implies: % 237.20/36.94 | (22) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & $i(v0) % 237.20/36.94 | & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ % 237.20/36.94 | $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : % 237.20/36.94 | (bit0(v1) = v4 & hBOOL(v5) = v6 & hBOOL(v2) = v3 & % 237.20/36.94 | hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 % 237.20/36.94 | = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, % 237.20/36.94 | v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 237.20/36.94 | any] : ? [v6: any] : (bit0(v1) = v3 & hBOOL(v4) = v5 & % 237.20/36.94 | hBOOL(v2) = v6 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & % 237.20/36.94 | ( ~ (v5 = 0) | v6 = 0)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_79_bin__less__0__simps_I1_J) implies: % 237.20/36.94 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 237.20/36.94 | hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & hBOOL(v1) = v2 & % 237.20/36.94 | hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0)) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_84_less__special_I4_J) implies: % 237.20/36.94 | (24) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.20/36.94 | ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? % 237.20/36.94 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 237.20/36.94 | : ? [v8: any] : (number_number_of_int(v1) = v5 & % 237.20/36.94 | hAPP_i1948725293t_bool(ord_less_int, v5) = v6 & hBOOL(v7) = v8 & % 237.20/36.94 | hBOOL(v3) = v4 & hAPP_int_bool(v6, one_one_int) = v7 & % 237.20/36.94 | hAPP_int_bool(v2, v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & % 237.20/36.94 | ( ~ (v4 = 0) | v8 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 237.20/36.94 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? % 237.20/36.94 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 237.20/36.94 | : ? [v8: any] : (number_number_of_int(v1) = v3 & % 237.20/36.94 | hAPP_i1948725293t_bool(ord_less_int, v3) = v4 & hBOOL(v7) = v8 & % 237.20/36.94 | hBOOL(v5) = v6 & hAPP_int_bool(v4, one_one_int) = v5 & % 237.20/36.94 | hAPP_int_bool(v2, v0) = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 237.20/36.94 | ( ~ (v6 = 0) | v8 = 0)))) % 237.20/36.94 | % 237.20/36.94 | ALPHA: (fact_85_less__special_I4_J) implies: % 237.20/36.95 | (25) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.20/36.95 | ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? % 237.20/36.95 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 237.20/36.95 | : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_real, v5) = v6 & % 237.20/36.95 | number267125858f_real(v1) = v5 & hBOOL(v7) = v8 & hBOOL(v3) = v4 % 237.20/36.95 | & hAPP_real_bool(v6, one_one_real) = v7 & hAPP_int_bool(v2, v0) % 237.20/36.95 | = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v8 = % 237.20/36.95 | 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 237.20/36.95 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? % 237.20/36.95 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 237.20/36.95 | : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_real, v3) = v4 & % 237.20/36.95 | number267125858f_real(v1) = v3 & hBOOL(v7) = v8 & hBOOL(v5) = v6 % 237.20/36.95 | & hAPP_real_bool(v4, one_one_real) = v5 & hAPP_int_bool(v2, v0) % 237.20/36.95 | = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v8 = % 237.20/36.95 | 0)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_86_less__special_I2_J) implies: % 237.20/36.95 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v1 & % 237.20/36.95 | hAPP_i1948725293t_bool(ord_less_int, v1) = v2 & % 237.20/36.95 | hAPP_i1948725293t_bool(ord_less_int, one_one_int) = v0 & $i(v2) & % 237.20/36.95 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, % 237.20/36.95 | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: % 237.20/36.95 | $i] : ? [v8: any] : (number_number_of_int(v3) = v6 & hBOOL(v7) % 237.20/36.95 | = v8 & hBOOL(v4) = v5 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & % 237.20/36.95 | $i(v6) & ( ~ (v5 = 0) | v8 = 0))) & ! [v3: $i] : ! [v4: $i] : % 237.20/36.95 | ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: % 237.20/36.95 | $i] : ? [v7: any] : ? [v8: any] : (number_number_of_int(v3) = % 237.20/36.95 | v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & hAPP_int_bool(v0, v5) = % 237.20/36.95 | v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = 0)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_87_less__special_I2_J) implies: % 237.20/36.95 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 237.20/36.95 | (hAPP_r1134773055l_bool(ord_less_real, one_one_real) = v0 & bit1(pls) % 237.20/36.95 | = v1 & hAPP_i1948725293t_bool(ord_less_int, v1) = v2 & $i(v2) & % 237.20/36.95 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, % 237.20/36.95 | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: % 237.20/36.95 | $i] : ? [v8: any] : (number267125858f_real(v3) = v6 & hBOOL(v7) % 237.20/36.95 | = v8 & hBOOL(v4) = v5 & hAPP_real_bool(v0, v6) = v7 & $i(v7) & % 237.20/36.95 | $i(v6) & ( ~ (v5 = 0) | v8 = 0))) & ! [v3: $i] : ! [v4: $i] : % 237.20/36.95 | ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: % 237.20/36.95 | $i] : ? [v7: any] : ? [v8: any] : (number267125858f_real(v3) = % 237.20/36.95 | v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & hAPP_real_bool(v0, v5) = % 237.20/36.95 | v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = 0)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_88_odd__less__0) implies: % 237.20/36.95 | (28) ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] % 237.20/36.95 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) = % 237.20/36.95 | v3) | ~ (hAPP_int_int(v3, v1) = v4) | ~ (hAPP_int_int(v0, v1) % 237.20/36.95 | = v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 237.20/36.95 | ? [v8: $i] : ? [v9: $i] : ? [v10: any] : % 237.20/36.95 | (hAPP_i1948725293t_bool(ord_less_int, v4) = v8 & % 237.20/36.95 | hAPP_i1948725293t_bool(ord_less_int, v1) = v5 & hBOOL(v9) = v10 % 237.20/36.95 | & hBOOL(v6) = v7 & hAPP_int_bool(v8, zero_zero_int) = v9 & % 237.20/36.95 | hAPP_int_bool(v5, zero_zero_int) = v6 & $i(v9) & $i(v8) & $i(v6) % 237.20/36.95 | & $i(v5) & ( ~ (v7 = 0) | v10 = 0))) & ! [v1: $i] : ! [v2: $i] % 237.20/36.95 | : ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) = v3) | ~ % 237.20/36.95 | (hAPP_int_int(v3, v1) = v4) | ~ (hAPP_int_int(v0, v1) = v2) | ~ % 237.20/36.95 | $i(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : % 237.20/36.95 | ? [v9: $i] : ? [v10: any] : (hAPP_i1948725293t_bool(ord_less_int, % 237.20/36.95 | v4) = v5 & hAPP_i1948725293t_bool(ord_less_int, v1) = v8 & % 237.20/36.95 | hBOOL(v9) = v10 & hBOOL(v6) = v7 & hAPP_int_bool(v8, % 237.20/36.95 | zero_zero_int) = v9 & hAPP_int_bool(v5, zero_zero_int) = v6 & % 237.20/36.95 | $i(v9) & $i(v8) & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v10 = 0)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_98_Pls__def) implies: % 237.20/36.95 | (29) pls = zero_zero_int % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_35_zero__is__num__zero) implies: % 237.20/36.95 | (30) number_number_of_int(pls) = zero_zero_int % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_113_add__numeral__0) implies: % 237.20/36.95 | (31) ? [v0: $i] : ? [v1: $i] : (number_number_of_int(pls) = v0 & % 237.20/36.95 | plus_plus_int(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.20/36.95 | : (v3 = v2 | ~ (hAPP_int_int(v1, v2) = v3) | ~ $i(v2))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_115_add__numeral__0__right) implies: % 237.20/36.95 | (32) ? [v0: $i] : (number_number_of_int(pls) = v0 & $i(v0) & ! [v1: $i] : % 237.20/36.95 | ! [v2: $i] : ( ~ (plus_plus_int(v1) = v2) | ~ $i(v1) | % 237.20/36.95 | hAPP_int_int(v2, v0) = v1)) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_117_power__eq__0__iff__number__of) implies: % 237.20/36.95 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 237.20/36.95 | (number_number_of_nat(v1) = v3) | ~ (power_power_int(v0) = v2) | ~ % 237.20/36.95 | (hAPP_nat_int(v2, v3) = zero_zero_int) | ~ $i(v1) | ~ $i(v0) | (v0 % 237.20/36.95 | = zero_zero_int & ~ (v3 = zero_zero_nat))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_128_Bit1__def) implies: % 237.20/36.95 | (34) ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] % 237.20/36.95 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (plus_plus_int(v2) = % 237.20/36.95 | v3) | ~ (hAPP_int_int(v3, v1) = v4) | ~ (hAPP_int_int(v0, v1) % 237.20/36.95 | = v2) | ~ $i(v1) | (bit1(v1) = v4 & $i(v4)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_129_odd__nonzero) implies: % 237.20/36.95 | (35) ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] % 237.20/36.95 | : ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus_int(v2) = v3) | ~ % 237.20/36.95 | (hAPP_int_int(v3, v1) = zero_zero_int) | ~ (hAPP_int_int(v0, v1) % 237.20/36.95 | = v2) | ~ $i(v1))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_131_number__of__int) implies: % 237.20/36.95 | (36) ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, % 237.20/36.95 | v0) = v1) | ~ $i(v0) | (number_number_of_int(v1) = v1 & % 237.20/36.95 | $i(v1))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_133_zero__less__power2) implies: % 237.20/36.95 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.20/36.95 | v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.20/36.95 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v3) & % 237.20/36.95 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v4 = % 237.20/36.95 | zero_zero_int | ~ (power_power_int(v4) = v5) | ~ $i(v4) | ? % 237.20/36.95 | [v6: $i] : ? [v7: $i] : (hAPP_nat_int(v5, v3) = v6 & hBOOL(v7) = % 237.20/36.95 | 0 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6))) & ! [v4: $i] % 237.20/36.95 | : ( ~ (power_power_int(zero_zero_int) = v4) | ? [v5: $i] : ? [v6: % 237.20/36.95 | $i] : ? [v7: int] : ( ~ (v7 = 0) & hAPP_nat_int(v4, v3) = v5 & % 237.20/36.95 | hBOOL(v6) = v7 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5)))) % 237.20/36.95 | % 237.20/36.95 | ALPHA: (fact_134_zero__less__power2) implies: % 237.20/36.96 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.20/36.96 | (hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = v0 & % 237.20/36.96 | bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.20/36.96 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v4 % 237.20/36.96 | = zero_zero_real | ~ (power_power_real(v4) = v5) | ~ $i(v4) | ? % 237.20/36.96 | [v6: $i] : ? [v7: $i] : (hAPP_nat_real(v5, v3) = v6 & hBOOL(v7) = % 237.20/36.96 | 0 & hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6))) & ! [v4: % 237.20/36.96 | $i] : ( ~ (power_power_real(zero_zero_real) = v4) | ? [v5: $i] : % 237.20/36.96 | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & hAPP_nat_real(v4, v3) = % 237.20/36.96 | v5 & hBOOL(v6) = v7 & hAPP_real_bool(v0, v5) = v6 & $i(v6) & % 237.20/36.96 | $i(v5)))) % 237.20/36.96 | % 237.20/36.96 | ALPHA: (fact_135_power2__less__0) implies: % 237.20/36.96 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.20/36.96 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.20/36.96 | [v3: $i] : ! [v4: $i] : ( ~ (power_power_int(v3) = v4) | ~ $i(v3) % 237.20/36.96 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 % 237.20/36.96 | = 0) & hAPP_i1948725293t_bool(ord_less_int, v5) = v6 & % 237.20/36.96 | hAPP_nat_int(v4, v2) = v5 & hBOOL(v7) = v8 & hAPP_int_bool(v6, % 237.20/36.96 | zero_zero_int) = v7 & $i(v7) & $i(v6) & $i(v5)))) % 237.20/36.96 | % 237.20/36.96 | ALPHA: (fact_136_power2__less__0) implies: % 237.30/36.96 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.30/36.96 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/36.96 | [v3: $i] : ! [v4: $i] : ( ~ (power_power_real(v3) = v4) | ~ $i(v3) % 237.30/36.96 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 % 237.30/36.96 | = 0) & hAPP_r1134773055l_bool(ord_less_real, v5) = v6 & % 237.30/36.96 | hAPP_nat_real(v4, v2) = v5 & hBOOL(v7) = v8 & hAPP_real_bool(v6, % 237.30/36.96 | zero_zero_real) = v7 & $i(v7) & $i(v6) & $i(v5)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_137_sum__power2__gt__zero__iff) implies: % 237.30/36.96 | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/36.96 | v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/36.96 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v3) & % 237.30/36.96 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 237.30/36.96 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 237.30/36.96 | $i] : ( ~ (power_power_int(v5) = v9) | ~ (power_power_int(v4) = % 237.30/36.96 | v6) | ~ (plus_plus_int(v7) = v8) | ~ (hAPP_nat_int(v9, v3) = % 237.30/36.96 | v10) | ~ (hAPP_nat_int(v6, v3) = v7) | ~ (hAPP_int_int(v8, % 237.30/36.96 | v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i] : % 237.30/36.96 | (hBOOL(v12) = 0 & hAPP_int_bool(v0, v11) = v12 & $i(v12)) | (v5 = % 237.30/36.96 | zero_zero_int & v4 = zero_zero_int)) & ! [v4: $i] : ! [v5: $i] % 237.30/36.96 | : ! [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(zero_zero_int) = % 237.30/36.96 | v4) | ~ (plus_plus_int(v5) = v6) | ~ (hAPP_nat_int(v4, v3) = % 237.30/36.96 | v5) | ~ (hAPP_int_int(v6, v5) = v7) | ? [v8: $i] : ? [v9: % 237.30/36.96 | int] : ( ~ (v9 = 0) & hBOOL(v8) = v9 & hAPP_int_bool(v0, v7) = % 237.30/36.96 | v8 & $i(v8)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_138_sum__power2__gt__zero__iff) implies: % 237.30/36.96 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.96 | (hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = v0 & % 237.30/36.96 | bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/36.96 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/36.96 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/36.96 | ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 237.30/36.96 | (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 237.30/36.96 | (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | % 237.30/36.96 | ~ (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/36.96 | [v12: $i] : (hBOOL(v12) = 0 & hAPP_real_bool(v0, v11) = v12 & % 237.30/36.96 | $i(v12)) | (v5 = zero_zero_real & v4 = zero_zero_real)) & ! % 237.30/36.96 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 237.30/36.96 | (plus_plus_real(v5) = v6) | ~ (power_power_real(zero_zero_real) = % 237.30/36.96 | v4) | ~ (hAPP_nat_real(v4, v3) = v5) | ~ (hAPP_real_real(v6, % 237.30/36.96 | v5) = v7) | ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & % 237.30/36.96 | hBOOL(v8) = v9 & hAPP_real_bool(v0, v7) = v8 & $i(v8)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_139_not__sum__power2__lt__zero) implies: % 237.30/36.96 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.30/36.96 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/36.96 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 237.30/36.96 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (power_power_int(v4) = % 237.30/36.96 | v8) | ~ (power_power_int(v3) = v5) | ~ (plus_plus_int(v6) = % 237.30/36.96 | v7) | ~ (hAPP_nat_int(v8, v2) = v9) | ~ (hAPP_nat_int(v5, v2) % 237.30/36.96 | = v6) | ~ (hAPP_int_int(v7, v9) = v10) | ~ $i(v4) | ~ $i(v3) % 237.30/36.96 | | ? [v11: $i] : ? [v12: $i] : ? [v13: int] : ( ~ (v13 = 0) & % 237.30/36.96 | hAPP_i1948725293t_bool(ord_less_int, v10) = v11 & hBOOL(v12) = % 237.30/36.96 | v13 & hAPP_int_bool(v11, zero_zero_int) = v12 & $i(v12) & % 237.30/36.96 | $i(v11)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_140_not__sum__power2__lt__zero) implies: % 237.30/36.96 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.30/36.96 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/36.96 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 237.30/36.96 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ (plus_plus_real(v6) = % 237.30/36.96 | v7) | ~ (power_power_real(v4) = v8) | ~ (power_power_real(v3) % 237.30/36.96 | = v5) | ~ (hAPP_nat_real(v8, v2) = v9) | ~ (hAPP_nat_real(v5, % 237.30/36.96 | v2) = v6) | ~ (hAPP_real_real(v7, v9) = v10) | ~ $i(v4) | ~ % 237.30/36.96 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: int] : ( ~ (v13 = % 237.30/36.96 | 0) & hAPP_r1134773055l_bool(ord_less_real, v10) = v11 & % 237.30/36.96 | hBOOL(v12) = v13 & hAPP_real_bool(v11, zero_zero_real) = v12 & % 237.30/36.96 | $i(v12) & $i(v11)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_143_number__of__Bit1) implies: % 237.30/36.96 | (45) ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] % 237.30/36.96 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 237.30/36.96 | (number_number_of_int(v1) = v2) | ~ (plus_plus_int(v3) = v4) | ~ % 237.30/36.96 | (hAPP_int_int(v4, v2) = v5) | ~ (hAPP_int_int(v0, v2) = v3) | ~ % 237.30/36.96 | $i(v1) | ? [v6: $i] : (number_number_of_int(v6) = v5 & bit1(v1) = % 237.30/36.96 | v6 & $i(v6) & $i(v5)))) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_53_one__is__num__one) implies: % 237.30/36.96 | (46) ? [v0: $i] : (number_number_of_int(v0) = one_one_int & bit1(pls) = v0 % 237.30/36.96 | & $i(v0)) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_55_Numeral1__eq1__nat) implies: % 237.30/36.96 | (47) ? [v0: $i] : (bit1(pls) = v0 & number_number_of_nat(v0) = one_one_nat % 237.30/36.96 | & $i(v0)) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_28_numeral__1__eq__1) implies: % 237.30/36.96 | (48) ? [v0: $i] : (number267125858f_real(v0) = one_one_real & bit1(pls) = % 237.30/36.96 | v0 & $i(v0)) % 237.30/36.96 | % 237.30/36.96 | ALPHA: (fact_148_mn) implies: % 237.30/36.97 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.30/36.97 | (hAPP_i1948725293t_bool(ord_less_int, m1) = v0 & % 237.30/36.97 | plus_plus_int(one_one_int) = v1 & % 237.30/36.97 | hAPP_nat_int(semiri1621563631at_int, n) = v2 & hAPP_int_int(v1, v2) % 237.30/36.97 | = v3 & hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) % 237.30/36.97 | & $i(v2) & $i(v1) & $i(v0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_149_of__nat__less__two__power) implies: % 237.30/36.97 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (number_number_of_int(v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & % 237.30/36.97 | power_power_int(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/36.97 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 237.30/36.97 | ~ (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~ % 237.30/36.97 | (hAPP_nat_int(v3, v4) = v7) | ~ % 237.30/36.97 | (hAPP_nat_int(semiri1621563631at_int, v4) = v5) | ~ % 237.30/36.97 | (hAPP_int_bool(v6, v7) = v8) | ~ $i(v4) | hBOOL(v8) = 0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_150_of__nat__less__two__power) implies: % 237.30/36.97 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (number267125858f_real(v1) = v2 & power_power_real(v2) = v3 & % 237.30/36.97 | bit1(pls) = v0 & bit0(v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 237.30/36.97 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 237.30/36.97 | : ( ~ (hAPP_r1134773055l_bool(ord_less_real, v5) = v6) | ~ % 237.30/36.97 | (hAPP_nat_real(v3, v4) = v7) | ~ % 237.30/36.97 | (hAPP_nat_real(semiri132038758t_real, v4) = v5) | ~ % 237.30/36.97 | (hAPP_real_bool(v6, v7) = v8) | ~ $i(v4) | hBOOL(v8) = 0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_151_transfer__int__nat__numerals_I3_J) implies: % 237.30/36.97 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (number_number_of_int(v1) = v2 & bit1(pls) = v0 & bit0(v0) = v1 & % 237.30/36.97 | number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int, % 237.30/36.97 | v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_152_transfer__int__nat__numerals_I4_J) implies: % 237.30/36.97 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (number_number_of_int(v1) = v2 & bit1(v0) = v1 & bit1(pls) = v0 & % 237.30/36.97 | number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int, % 237.30/36.97 | v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_3_sum__power2__eq__zero__iff) implies: % 237.30/36.97 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.30/36.97 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/36.97 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 237.30/36.97 | ! [v8: $i] : ! [v9: $i] : ( ~ (plus_plus_real(v6) = v7) | ~ % 237.30/36.97 | (power_power_real(v4) = v8) | ~ (power_power_real(v3) = v5) | ~ % 237.30/36.97 | (hAPP_nat_real(v8, v2) = v9) | ~ (hAPP_nat_real(v5, v2) = v6) | % 237.30/36.97 | ~ (hAPP_real_real(v7, v9) = zero_zero_real) | ~ $i(v4) | ~ % 237.30/36.97 | $i(v3) | (v4 = zero_zero_real & v3 = zero_zero_real)) & ! [v3: % 237.30/36.97 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = % 237.30/36.97 | zero_zero_real | ~ (plus_plus_real(v4) = v5) | ~ % 237.30/36.97 | (power_power_real(zero_zero_real) = v3) | ~ (hAPP_nat_real(v3, % 237.30/36.97 | v2) = v4) | ~ (hAPP_real_real(v5, v4) = v6))) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_163_power__strict__decreasing) implies: % 237.30/36.97 | (55) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/36.97 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 237.30/36.97 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 237.30/36.97 | (power_power_int(v1) = v4) | ~ % 237.30/36.97 | (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~ % 237.30/36.97 | (hAPP_nat_int(v4, v3) = v5) | ~ (hAPP_nat_int(v4, v2) = v7) | ~ % 237.30/36.97 | (hAPP_int_bool(v6, v7) = v8) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 237.30/36.97 | ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? % 237.30/36.97 | [v13: any] : ? [v14: $i] : ? [v15: $i] : ? [v16: any] : ? % 237.30/36.97 | [v17: any] : (hAPP_n1699378549t_bool(ord_less_nat, v2) = v9 & % 237.30/36.97 | hAPP_i1948725293t_bool(ord_less_int, v1) = v14 & hBOOL(v15) = % 237.30/36.97 | v16 & hBOOL(v12) = v13 & hBOOL(v10) = v11 & hBOOL(v8) = v17 & % 237.30/36.97 | hAPP_nat_bool(v9, v3) = v10 & hAPP_int_bool(v14, one_one_int) = % 237.30/36.97 | v15 & hAPP_int_bool(v0, v1) = v12 & $i(v15) & $i(v14) & $i(v12) % 237.30/36.97 | & $i(v10) & $i(v9) & ( ~ (v16 = 0) | ~ (v13 = 0) | ~ (v11 = 0) % 237.30/36.97 | | v17 = 0)))) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_166_zero__less__two) implies: % 237.30/36.97 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & % 237.30/36.97 | plus_plus_int(one_one_int) = v1 & hAPP_int_int(v1, one_one_int) = v2 % 237.30/36.97 | & hBOOL(v3) = 0 & hAPP_int_bool(v0, v2) = v3 & $i(v3) & $i(v2) & % 237.30/36.97 | $i(v1) & $i(v0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_167_zero__less__two) implies: % 237.30/36.97 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/36.97 | (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v0 & % 237.30/36.97 | plus_plus_nat(one_one_nat) = v1 & hAPP_nat_nat(v1, one_one_nat) = v2 % 237.30/36.97 | & hBOOL(v3) = 0 & hAPP_nat_bool(v0, v2) = v3 & $i(v3) & $i(v2) & % 237.30/36.97 | $i(v1) & $i(v0)) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_207_less__nat__number__of) implies: % 237.30/36.97 | (58) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & $i(v0) % 237.30/36.97 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 237.30/36.97 | $i] : ! [v6: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_nat, v3) % 237.30/36.97 | = v4) | ~ (number_number_of_nat(v2) = v5) | ~ % 237.30/36.97 | (number_number_of_nat(v1) = v3) | ~ (hAPP_nat_bool(v4, v5) = v6) % 237.30/36.97 | | ~ $i(v2) | ~ $i(v1) | ? [v7: any] : ? [v8: $i] : ? [v9: $i] % 237.30/36.97 | : ? [v10: any] : ? [v11: $i] : ? [v12: any] : % 237.30/36.97 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v8 & hBOOL(v11) = v12 % 237.30/36.97 | & hBOOL(v9) = v10 & hBOOL(v6) = v7 & hAPP_int_bool(v8, v2) = v9 % 237.30/36.97 | & hAPP_int_bool(v0, v2) = v11 & $i(v11) & $i(v9) & $i(v8) & ( ~ % 237.30/36.97 | (v7 = 0) | (v12 = 0 & v10 = 0)))) & ! [v1: $i] : ! [v2: $i] % 237.30/36.97 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.30/36.97 | (hAPP_n1699378549t_bool(ord_less_nat, v3) = v4) | ~ % 237.30/36.97 | (number_number_of_nat(v2) = v5) | ~ (number_number_of_nat(v1) = % 237.30/36.97 | v3) | ~ (hAPP_nat_bool(v4, v5) = v6) | ~ $i(v2) | ~ $i(v1) | % 237.30/36.97 | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: % 237.30/36.97 | any] : ? [v12: any] : (hAPP_i1948725293t_bool(ord_less_int, v1) % 237.30/36.97 | = v7 & hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v6) = v12 & % 237.30/36.97 | hAPP_int_bool(v7, v2) = v8 & hAPP_int_bool(v0, v2) = v10 & % 237.30/36.97 | $i(v10) & $i(v8) & $i(v7) & ( ~ (v11 = 0) | ~ (v9 = 0) | v12 = % 237.30/36.97 | 0)))) % 237.30/36.97 | % 237.30/36.97 | ALPHA: (fact_222_less__0__number__of) implies: % 237.30/36.98 | (59) ? [v0: $i] : ? [v1: $i] : (hAPP_n1699378549t_bool(ord_less_nat, % 237.30/36.98 | zero_zero_nat) = v0 & hAPP_i1948725293t_bool(ord_less_int, pls) = % 237.30/36.98 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 237.30/36.98 | (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 237.30/36.98 | $i] : ? [v6: $i] : ? [v7: any] : (number_number_of_nat(v2) = % 237.30/36.98 | v5 & hBOOL(v6) = v7 & hBOOL(v3) = v4 & hAPP_nat_bool(v0, v5) = % 237.30/36.98 | v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = 0))) & ! [v2: $i] : % 237.30/36.98 | ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: % 237.30/36.98 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 237.30/36.98 | (number_number_of_nat(v2) = v4 & hBOOL(v5) = v6 & hBOOL(v3) = v7 & % 237.30/36.98 | hAPP_nat_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | v7 % 237.30/36.98 | = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_223_zero__less__int__conv) implies: % 237.30/36.98 | (60) ? [v0: $i] : ? [v1: $i] : (hAPP_n1699378549t_bool(ord_less_nat, % 237.30/36.98 | zero_zero_nat) = v1 & hAPP_i1948725293t_bool(ord_less_int, % 237.30/36.98 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.30/36.98 | : ( ~ (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 237.30/36.98 | [v5: $i] : ? [v6: $i] : ? [v7: any] : % 237.30/36.98 | (hAPP_nat_int(semiri1621563631at_int, v2) = v5 & hBOOL(v6) = v7 & % 237.30/36.98 | hBOOL(v3) = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & % 237.30/36.98 | ( ~ (v4 = 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 237.30/36.98 | (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: % 237.30/36.98 | $i] : ? [v6: any] : ? [v7: any] : % 237.30/36.98 | (hAPP_nat_int(semiri1621563631at_int, v2) = v4 & hBOOL(v5) = v6 & % 237.30/36.98 | hBOOL(v3) = v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & % 237.30/36.98 | ( ~ (v6 = 0) | v7 = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_40_int__1) implies: % 237.30/36.98 | (61) hAPP_nat_int(semiri1621563631at_int, one_one_nat) = one_one_int % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_258_pos__add__strict) implies: % 237.30/36.98 | (62) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/36.98 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 237.30/36.98 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 237.30/36.98 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ % 237.30/36.98 | (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 237.30/36.98 | (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 237.30/36.98 | ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? % 237.30/36.98 | [v12: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v7) = v12 % 237.30/36.98 | & hAPP_int_bool(v4, v2) = v10 & hAPP_int_bool(v0, v3) = v8 & % 237.30/36.98 | $i(v10) & $i(v8) & ( ~ (v11 = 0) | ~ (v9 = 0) | v12 = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_81_int__0__less__1) implies: % 237.30/36.98 | (63) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int, % 237.30/36.98 | zero_zero_int) = v0 & hBOOL(v1) = 0 & hAPP_int_bool(v0, % 237.30/36.98 | one_one_int) = v1 & $i(v1) & $i(v0)) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_267_zero__less__power) implies: % 237.30/36.98 | (64) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/36.98 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 237.30/36.98 | : ( ~ (power_power_int(v2) = v3) | ~ (hAPP_nat_int(v3, v1) = v4) | % 237.30/36.98 | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : % 237.30/36.98 | ? [v8: any] : (hBOOL(v7) = v8 & hBOOL(v5) = v6 & hAPP_int_bool(v0, % 237.30/36.98 | v4) = v7 & hAPP_int_bool(v0, v2) = v5 & $i(v7) & $i(v5) & ( ~ % 237.30/36.98 | (v6 = 0) | v8 = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_296_pos2) implies: % 237.30/36.98 | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.30/36.98 | (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v0 & bit1(pls) % 237.30/36.98 | = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & hBOOL(v4) = 0 % 237.30/36.98 | & hAPP_nat_bool(v0, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 237.30/36.98 | $i(v0)) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_297_zero__less__imp__eq__int) implies: % 237.30/36.98 | (66) ? [v0: $i] : ? [v1: $i] : (hAPP_n1699378549t_bool(ord_less_nat, % 237.30/36.98 | zero_zero_nat) = v1 & hAPP_i1948725293t_bool(ord_less_int, % 237.30/36.98 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.30/36.98 | : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? % 237.30/36.98 | [v5: $i] : (hAPP_nat_int(semiri1621563631at_int, v4) = v2 & % 237.30/36.98 | hBOOL(v5) = 0 & hAPP_nat_bool(v1, v4) = v5 & $i(v5) & $i(v4)) | % 237.30/36.98 | ? [v4: int] : ( ~ (v4 = 0) & hBOOL(v3) = v4))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_304_zero__less__double__add__iff__zero__less__single__add) % 237.30/36.98 | implies: % 237.30/36.98 | (67) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/36.98 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) % 237.30/36.98 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 237.30/36.98 | ? [v6: $i] : ? [v7: any] : (plus_plus_int(v1) = v4 & % 237.30/36.98 | hAPP_int_int(v4, v1) = v5 & hBOOL(v6) = v7 & hBOOL(v2) = v3 & % 237.30/36.98 | hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 % 237.30/36.98 | = 0) | v7 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 237.30/36.98 | (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: % 237.30/36.98 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 237.30/36.98 | (plus_plus_int(v1) = v3 & hAPP_int_int(v3, v1) = v4 & hBOOL(v5) = % 237.30/36.98 | v6 & hBOOL(v2) = v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & % 237.30/36.98 | $i(v4) & $i(v3) & ( ~ (v6 = 0) | v7 = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_402_add__pos__pos) implies: % 237.30/36.98 | (68) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/36.98 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 237.30/36.98 | : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ (hAPP_int_bool(v0, v1) = v4) % 237.30/36.98 | | ~ $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: % 237.30/36.98 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : % 237.30/36.98 | (plus_plus_int(v2) = v7 & hAPP_int_int(v7, v1) = v8 & hBOOL(v9) = % 237.30/36.98 | v10 & hBOOL(v4) = v6 & hBOOL(v3) = v5 & hAPP_int_bool(v0, v8) = % 237.30/36.98 | v9 & $i(v9) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v10 % 237.30/36.98 | = 0)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_407_nat__1__add__number__of) implies: % 237.30/36.98 | (69) ? [v0: $i] : (plus_plus_nat(one_one_nat) = v0 & $i(v0) & ! [v1: $i] % 237.30/36.98 | : ! [v2: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) % 237.30/36.98 | | ~ $i(v1) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: % 237.30/36.98 | $i] : ? [v7: $i] : ? [v8: $i] : (succ(v1) = v7 & % 237.30/36.98 | hAPP_nat_nat(v0, v5) = v6 & number_number_of_nat(v7) = v8 & % 237.30/36.98 | number_number_of_nat(v1) = v5 & hBOOL(v3) = v4 & % 237.30/36.98 | hAPP_int_bool(v2, pls) = v3 & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 237.30/36.98 | & $i(v3) & (v8 = v6 | v4 = 0))) & ! [v1: $i] : ! [v2: $i] : ( % 237.30/36.98 | ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ $i(v1) | ? % 237.30/36.98 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 237.30/36.98 | (hAPP_nat_nat(v0, v5) = v6 & number_number_of_nat(v1) = v5 & % 237.30/36.98 | hBOOL(v3) = v4 & hAPP_int_bool(v2, pls) = v3 & $i(v6) & $i(v5) & % 237.30/36.98 | $i(v3) & ( ~ (v4 = 0) | v6 = one_one_nat)))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_447_zless__le) implies: % 237.30/36.98 | (70) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 237.30/36.98 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v2) | ~ % 237.30/36.98 | (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 237.30/36.98 | : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 237.30/36.98 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v5 & hBOOL(v6) = v7 & % 237.30/36.98 | hBOOL(v3) = v4 & hAPP_int_bool(v5, v1) = v6 & $i(v6) & $i(v5) & ( % 237.30/36.98 | ~ (v4 = 0) | (v7 = 0 & ~ (v1 = v0))))) % 237.30/36.98 | % 237.30/36.98 | ALPHA: (fact_463_le__special_I2_J) implies: % 237.30/36.99 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 237.30/36.99 | (hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = v0 & % 237.30/36.99 | bit1(pls) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2 & % 237.30/36.99 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 237.30/36.99 | (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 237.30/36.99 | $i] : ? [v7: $i] : ? [v8: any] : (number267125858f_real(v3) = % 237.30/36.99 | v6 & hBOOL(v7) = v8 & hBOOL(v4) = v5 & hAPP_real_bool(v0, v6) = % 237.30/36.99 | v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 = 0))) & ! [v3: $i] : % 237.30/36.99 | ! [v4: $i] : ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: % 237.30/36.99 | $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 237.30/36.99 | (number267125858f_real(v3) = v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 % 237.30/36.99 | & hAPP_real_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | % 237.30/36.99 | v8 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_464_le__special_I2_J) implies: % 237.30/36.99 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v1 & % 237.30/36.99 | hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2 & % 237.30/36.99 | hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v0 & $i(v2) & % 237.30/36.99 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v2, % 237.30/36.99 | v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: % 237.30/36.99 | $i] : ? [v8: any] : (number_number_of_int(v3) = v6 & hBOOL(v7) % 237.30/36.99 | = v8 & hBOOL(v4) = v5 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & % 237.30/36.99 | $i(v6) & ( ~ (v5 = 0) | v8 = 0))) & ! [v3: $i] : ! [v4: $i] : % 237.30/36.99 | ( ~ (hAPP_int_bool(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: % 237.30/36.99 | $i] : ? [v7: any] : ? [v8: any] : (number_number_of_int(v3) = % 237.30/36.99 | v5 & hBOOL(v6) = v7 & hBOOL(v4) = v8 & hAPP_int_bool(v0, v5) = % 237.30/36.99 | v6 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | v8 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_465_le__special_I4_J) implies: % 237.30/36.99 | (73) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.30/36.99 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | % 237.30/36.99 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 237.30/36.99 | $i] : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 237.30/36.99 | v5) = v6 & number267125858f_real(v1) = v5 & hBOOL(v7) = v8 & % 237.30/36.99 | hBOOL(v3) = v4 & hAPP_real_bool(v6, one_one_real) = v7 & % 237.30/36.99 | hAPP_int_bool(v2, v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & % 237.30/36.99 | ( ~ (v4 = 0) | v8 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 237.30/36.99 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | % 237.30/36.99 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: % 237.30/36.99 | $i] : ? [v8: any] : (hAPP_r1134773055l_bool(ord_less_eq_real, % 237.30/36.99 | v3) = v4 & number267125858f_real(v1) = v3 & hBOOL(v7) = v8 & % 237.30/36.99 | hBOOL(v5) = v6 & hAPP_real_bool(v4, one_one_real) = v5 & % 237.30/36.99 | hAPP_int_bool(v2, v0) = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 237.30/36.99 | ( ~ (v6 = 0) | v8 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_466_le__special_I4_J) implies: % 237.30/36.99 | (74) ? [v0: $i] : (bit1(pls) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 237.30/36.99 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | % 237.30/36.99 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 237.30/36.99 | $i] : ? [v8: any] : (number_number_of_int(v1) = v5 & % 237.30/36.99 | hAPP_i1948725293t_bool(ord_less_eq_int, v5) = v6 & hBOOL(v7) = % 237.30/36.99 | v8 & hBOOL(v3) = v4 & hAPP_int_bool(v6, one_one_int) = v7 & % 237.30/36.99 | hAPP_int_bool(v2, v0) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v3) & % 237.30/36.99 | ( ~ (v4 = 0) | v8 = 0))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 237.30/36.99 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v2) | ~ $i(v1) | % 237.30/36.99 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: % 237.30/36.99 | $i] : ? [v8: any] : (number_number_of_int(v1) = v3 & % 237.30/36.99 | hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4 & hBOOL(v7) = % 237.30/36.99 | v8 & hBOOL(v5) = v6 & hAPP_int_bool(v4, one_one_int) = v5 & % 237.30/36.99 | hAPP_int_bool(v2, v0) = v7 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & % 237.30/36.99 | ( ~ (v6 = 0) | v8 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_531_semiring__1__add__number__of) implies: % 237.30/36.99 | (75) ? [v0: $i] : ? [v1: $i] : (plus_plus_nat(one_one_nat) = v1 & % 237.30/36.99 | hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v0 & $i(v1) & $i(v0) % 237.30/36.99 | & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ % 237.30/36.99 | $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 237.30/36.99 | ? [v8: $i] : (succ(v2) = v7 & hAPP_nat_nat(v1, v5) = v6 & % 237.30/36.99 | number_number_of_nat(v7) = v8 & number_number_of_nat(v2) = v5 & % 237.30/36.99 | hBOOL(v3) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = % 237.30/36.99 | 0) | v8 = v6)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_532_semiring__1__add__number__of) implies: % 237.30/36.99 | (76) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/36.99 | pls) = v0 & plus_plus_int(one_one_int) = v1 & $i(v1) & $i(v0) & ! % 237.30/36.99 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ % 237.30/36.99 | $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 237.30/36.99 | ? [v8: $i] : (succ(v2) = v7 & number_number_of_int(v7) = v8 & % 237.30/36.99 | number_number_of_int(v2) = v5 & hAPP_int_int(v1, v5) = v6 & % 237.30/36.99 | hBOOL(v3) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = % 237.30/36.99 | 0) | v8 = v6)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_538_add__pos__nonneg) implies: % 237.30/36.99 | (77) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/36.99 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_int, % 237.30/36.99 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.30/36.99 | : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_int_bool(v1, v2) = v5) | ~ % 237.30/36.99 | (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: % 237.30/36.99 | any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 237.30/36.99 | ? [v11: any] : (plus_plus_int(v3) = v8 & hAPP_int_int(v8, v2) = % 237.30/36.99 | v9 & hBOOL(v10) = v11 & hBOOL(v5) = v7 & hBOOL(v4) = v6 & % 237.30/36.99 | hAPP_int_bool(v0, v9) = v10 & $i(v10) & $i(v9) & $i(v8) & ( ~ % 237.30/36.99 | (v7 = 0) | ~ (v6 = 0) | v11 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_541_add__nonneg__pos) implies: % 237.30/36.99 | (78) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/36.99 | zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_int, % 237.30/36.99 | zero_zero_int) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.30/36.99 | : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_int_bool(v1, v2) = v5) | ~ % 237.30/36.99 | (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: % 237.30/36.99 | any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 237.30/36.99 | ? [v11: any] : (plus_plus_int(v3) = v8 & hAPP_int_int(v8, v2) = % 237.30/36.99 | v9 & hBOOL(v10) = v11 & hBOOL(v5) = v7 & hBOOL(v4) = v6 & % 237.30/36.99 | hAPP_int_bool(v1, v9) = v10 & $i(v10) & $i(v9) & $i(v8) & ( ~ % 237.30/36.99 | (v7 = 0) | ~ (v6 = 0) | v11 = 0)))) % 237.30/36.99 | % 237.30/36.99 | ALPHA: (fact_544_add__strict__increasing) implies: % 237.30/37.00 | (79) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = % 237.30/37.00 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 237.30/37.00 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 237.30/37.00 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ % 237.30/37.00 | (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 237.30/37.00 | (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 237.30/37.00 | ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? % 237.30/37.00 | [v12: any] : ? [v13: any] : % 237.30/37.00 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v10 & hBOOL(v11) = % 237.30/37.00 | v12 & hBOOL(v8) = v9 & hBOOL(v7) = v13 & hAPP_int_bool(v10, v2) % 237.30/37.00 | = v11 & hAPP_int_bool(v0, v3) = v8 & $i(v11) & $i(v10) & $i(v8) % 237.30/37.00 | & ( ~ (v12 = 0) | ~ (v9 = 0) | v13 = 0)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_547_add__strict__increasing2) implies: % 237.30/37.00 | (80) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) % 237.30/37.00 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 237.30/37.00 | $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 237.30/37.00 | (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ % 237.30/37.00 | (plus_plus_int(v3) = v5) | ~ (hAPP_int_int(v5, v2) = v6) | ~ % 237.30/37.00 | (hAPP_int_bool(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 237.30/37.00 | ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ? % 237.30/37.00 | [v12: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v7) = v12 % 237.30/37.00 | & hAPP_int_bool(v4, v2) = v10 & hAPP_int_bool(v0, v3) = v8 & % 237.30/37.00 | $i(v10) & $i(v8) & ( ~ (v11 = 0) | ~ (v9 = 0) | v12 = 0)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_559_rel__simps_I5_J) implies: % 237.30/37.00 | (81) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/37.00 | pls) = v1 & hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & % 237.30/37.00 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, % 237.30/37.00 | v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: % 237.30/37.00 | $i] : ? [v7: any] : (bit1(v2) = v5 & hBOOL(v6) = v7 & hBOOL(v3) % 237.30/37.00 | = v4 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = % 237.30/37.00 | 0) | v7 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 237.30/37.00 | (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: % 237.30/37.00 | $i] : ? [v6: any] : ? [v7: any] : (bit1(v2) = v4 & hBOOL(v5) = % 237.30/37.00 | v6 & hBOOL(v3) = v7 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & % 237.30/37.00 | $i(v4) & ( ~ (v6 = 0) | v7 = 0)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_565_int__one__le__iff__zero__less) implies: % 237.30/37.00 | (82) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/37.00 | one_one_int) = v0 & hAPP_i1948725293t_bool(ord_less_int, % 237.30/37.00 | zero_zero_int) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 237.30/37.00 | : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 237.30/37.00 | [v5: $i] : ? [v6: any] : (hBOOL(v5) = v6 & hBOOL(v3) = v4 & % 237.30/37.00 | hAPP_int_bool(v1, v2) = v5 & $i(v5) & ( ~ (v4 = 0) | v6 = 0))) & % 237.30/37.00 | ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ % 237.30/37.00 | $i(v2) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : (hBOOL(v4) = % 237.30/37.00 | v5 & hBOOL(v3) = v6 & hAPP_int_bool(v1, v2) = v4 & $i(v4) & ( ~ % 237.30/37.00 | (v5 = 0) | v6 = 0)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_567_succ__Pls) implies: % 237.30/37.00 | (83) ? [v0: $i] : (succ(pls) = v0 & bit1(pls) = v0 & $i(v0)) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) % 237.30/37.00 | implies: % 237.30/37.00 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.30/37.00 | (number_number_of_int(v2) = v3 & bit1(v1) = v2 & bit1(pls) = v1 & % 237.30/37.00 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 237.30/37.00 | hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & % 237.30/37.00 | $i(v2) & $i(v1) & $i(v0)) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_581_le__imp__0__less) implies: % 237.30/37.00 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 237.30/37.00 | (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 237.30/37.00 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 & % 237.30/37.00 | plus_plus_int(one_one_int) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: % 237.30/37.00 | $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v0, v3) = v4) | ~ $i(v3) | % 237.30/37.00 | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 237.30/37.00 | (hAPP_int_int(v2, v3) = v6 & hBOOL(v7) = v8 & hBOOL(v4) = v5 & % 237.30/37.00 | hAPP_int_bool(v1, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v8 % 237.30/37.00 | = 0)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_583_number__of__succ) implies: % 237.30/37.00 | (86) ? [v0: $i] : (plus_plus_int(one_one_int) = v0 & $i(v0) & ! [v1: $i] % 237.30/37.00 | : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? % 237.30/37.00 | [v4: $i] : (number_number_of_int(v2) = v3 & % 237.30/37.00 | number_number_of_int(v1) = v4 & hAPP_int_int(v0, v4) = v3 & % 237.30/37.00 | $i(v4) & $i(v3)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) % 237.30/37.00 | implies: % 237.30/37.00 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.30/37.00 | (number_number_of_int(v2) = v3 & bit1(pls) = v1 & bit0(v1) = v2 & % 237.30/37.00 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 237.30/37.00 | hBOOL(v4) = 0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & % 237.30/37.00 | $i(v2) & $i(v1) & $i(v0)) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_589_power2__ge__self) implies: % 237.30/37.00 | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) = % 237.30/37.00 | v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 237.30/37.00 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 237.30/37.00 | ~ (power_power_int(v3) = v5) | ~ % 237.30/37.00 | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4) | ~ % 237.30/37.00 | (hAPP_nat_int(v5, v2) = v6) | ~ (hAPP_int_bool(v4, v6) = v7) | ~ % 237.30/37.00 | $i(v3) | hBOOL(v7) = 0)) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_590_zero__le__power2) implies: % 237.30/37.00 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.00 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v0 & % 237.30/37.00 | bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/37.00 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ % 237.30/37.00 | (power_power_real(v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: % 237.30/37.00 | $i] : (hAPP_nat_real(v5, v3) = v6 & hBOOL(v7) = 0 & % 237.30/37.00 | hAPP_real_bool(v0, v6) = v7 & $i(v7) & $i(v6)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_591_zero__le__power2) implies: % 237.30/37.00 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/37.00 | v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/37.00 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v3) % 237.30/37.00 | & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ % 237.30/37.00 | (power_power_int(v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] % 237.30/37.00 | : (hAPP_nat_int(v5, v3) = v6 & hBOOL(v7) = 0 & hAPP_int_bool(v0, % 237.30/37.00 | v6) = v7 & $i(v7) & $i(v6)))) % 237.30/37.00 | % 237.30/37.00 | ALPHA: (fact_592_power2__le__imp__le) implies: % 237.30/37.01 | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.01 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v3 & % 237.30/37.01 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.01 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.01 | ! [v11: $i] : ( ~ (hAPP_r1134773055l_bool(ord_less_eq_real, v7) = % 237.30/37.01 | v8) | ~ (power_power_real(v5) = v9) | ~ (power_power_real(v4) % 237.30/37.01 | = v6) | ~ (hAPP_nat_real(v9, v2) = v10) | ~ (hAPP_nat_real(v6, % 237.30/37.01 | v2) = v7) | ~ (hAPP_real_bool(v8, v10) = v11) | ~ $i(v5) | % 237.30/37.01 | ~ $i(v4) | ? [v12: any] : ? [v13: $i] : ? [v14: any] : ? [v15: % 237.30/37.01 | $i] : ? [v16: $i] : ? [v17: any] : % 237.30/37.01 | (hAPP_r1134773055l_bool(ord_less_eq_real, v4) = v15 & hBOOL(v16) = % 237.30/37.01 | v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_real_bool(v15, % 237.30/37.01 | v5) = v16 & hAPP_real_bool(v3, v5) = v13 & $i(v16) & $i(v15) & % 237.30/37.01 | $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 = 0)))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_593_power2__le__imp__le) implies: % 237.30/37.01 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.01 | (hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = v3 & % 237.30/37.01 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.01 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.01 | ! [v11: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_eq_nat, v7) = v8) % 237.30/37.01 | | ~ (power_power_nat(v5) = v9) | ~ (power_power_nat(v4) = v6) | % 237.30/37.01 | ~ (hAPP_nat_nat(v9, v2) = v10) | ~ (hAPP_nat_nat(v6, v2) = v7) | % 237.30/37.01 | ~ (hAPP_nat_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.01 | [v12: any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? % 237.30/37.01 | [v16: $i] : ? [v17: any] : % 237.30/37.01 | (hAPP_n1699378549t_bool(ord_less_eq_nat, v4) = v15 & hBOOL(v16) = % 237.30/37.01 | v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP_nat_bool(v15, % 237.30/37.01 | v5) = v16 & hAPP_nat_bool(v3, v5) = v13 & $i(v16) & $i(v15) & % 237.30/37.01 | $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 = 0)))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_594_power2__le__imp__le) implies: % 237.30/37.01 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/37.01 | v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v3 & $i(v3) % 237.30/37.01 | & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 237.30/37.01 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 237.30/37.01 | $i] : ( ~ (power_power_int(v5) = v9) | ~ (power_power_int(v4) = % 237.30/37.01 | v6) | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v7) = v8) | ~ % 237.30/37.01 | (hAPP_nat_int(v9, v2) = v10) | ~ (hAPP_nat_int(v6, v2) = v7) | ~ % 237.30/37.01 | (hAPP_int_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: % 237.30/37.01 | any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: % 237.30/37.01 | $i] : ? [v17: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.30/37.01 | v4) = v15 & hBOOL(v16) = v17 & hBOOL(v13) = v14 & hBOOL(v11) = % 237.30/37.01 | v12 & hAPP_int_bool(v15, v5) = v16 & hAPP_int_bool(v3, v5) = v13 % 237.30/37.01 | & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | % 237.30/37.01 | v17 = 0)))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_595_power2__eq__imp__eq) implies: % 237.30/37.01 | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.01 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v3 & % 237.30/37.01 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.01 | [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (hAPP_real_bool(v3, v5) = v7) % 237.30/37.01 | | ~ (hAPP_real_bool(v3, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.01 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 237.30/37.01 | any] : ? [v13: any] : (power_power_real(v5) = v10 & % 237.30/37.01 | power_power_real(v4) = v8 & hAPP_nat_real(v10, v2) = v11 & % 237.30/37.01 | hAPP_nat_real(v8, v2) = v9 & hBOOL(v7) = v13 & hBOOL(v6) = v12 & % 237.30/37.01 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v13 = 0) | ~ (v12 = % 237.30/37.01 | 0) | ~ (v11 = v9))))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_596_power2__eq__imp__eq) implies: % 237.30/37.01 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.01 | (hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = v3 & % 237.30/37.01 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.01 | [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (hAPP_nat_bool(v3, v5) = v7) % 237.30/37.01 | | ~ (hAPP_nat_bool(v3, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.01 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 237.30/37.01 | any] : ? [v13: any] : (power_power_nat(v5) = v10 & % 237.30/37.01 | power_power_nat(v4) = v8 & hAPP_nat_nat(v10, v2) = v11 & % 237.30/37.01 | hAPP_nat_nat(v8, v2) = v9 & hBOOL(v7) = v13 & hBOOL(v6) = v12 & % 237.30/37.01 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v13 = 0) | ~ (v12 = % 237.30/37.01 | 0) | ~ (v11 = v9))))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_597_power2__eq__imp__eq) implies: % 237.30/37.01 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/37.01 | v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v3 & $i(v3) % 237.30/37.01 | & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 237.30/37.01 | : ! [v7: $i] : (v5 = v4 | ~ (hAPP_int_bool(v3, v5) = v7) | ~ % 237.30/37.01 | (hAPP_int_bool(v3, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: $i] % 237.30/37.01 | : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: any] : ? % 237.30/37.01 | [v13: any] : (power_power_int(v5) = v10 & power_power_int(v4) = v8 % 237.30/37.01 | & hAPP_nat_int(v10, v2) = v11 & hAPP_nat_int(v8, v2) = v9 & % 237.30/37.01 | hBOOL(v7) = v13 & hBOOL(v6) = v12 & $i(v11) & $i(v10) & $i(v9) & % 237.30/37.01 | $i(v8) & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = v9))))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_600_power2__less__imp__less) implies: % 237.30/37.01 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.01 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v3 & % 237.30/37.01 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.01 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.01 | ! [v11: $i] : ( ~ (hAPP_r1134773055l_bool(ord_less_real, v7) = v8) | % 237.30/37.01 | ~ (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | % 237.30/37.01 | ~ (hAPP_nat_real(v9, v2) = v10) | ~ (hAPP_nat_real(v6, v2) = v7) % 237.30/37.01 | | ~ (hAPP_real_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.01 | [v12: any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? % 237.30/37.01 | [v16: $i] : ? [v17: any] : (hAPP_r1134773055l_bool(ord_less_real, % 237.30/37.01 | v4) = v15 & hBOOL(v16) = v17 & hBOOL(v13) = v14 & hBOOL(v11) = % 237.30/37.01 | v12 & hAPP_real_bool(v15, v5) = v16 & hAPP_real_bool(v3, v5) = % 237.30/37.01 | v13 & $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) % 237.30/37.01 | | v17 = 0)))) % 237.30/37.01 | % 237.30/37.01 | ALPHA: (fact_601_power2__less__imp__less) implies: % 237.30/37.02 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.02 | (hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = v3 & % 237.30/37.02 | bit1(pls) = v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.02 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.02 | ! [v11: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_nat, v7) = v8) | % 237.30/37.02 | ~ (power_power_nat(v5) = v9) | ~ (power_power_nat(v4) = v6) | ~ % 237.30/37.02 | (hAPP_nat_nat(v9, v2) = v10) | ~ (hAPP_nat_nat(v6, v2) = v7) | ~ % 237.30/37.02 | (hAPP_nat_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: % 237.30/37.02 | any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: % 237.30/37.02 | $i] : ? [v17: any] : (hAPP_n1699378549t_bool(ord_less_nat, v4) % 237.30/37.02 | = v15 & hBOOL(v16) = v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & % 237.30/37.02 | hAPP_nat_bool(v15, v5) = v16 & hAPP_nat_bool(v3, v5) = v13 & % 237.30/37.02 | $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 % 237.30/37.02 | = 0)))) % 237.30/37.02 | % 237.30/37.02 | ALPHA: (fact_602_power2__less__imp__less) implies: % 237.30/37.02 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/37.02 | v0 & bit0(v0) = v1 & number_number_of_nat(v1) = v2 & % 237.30/37.02 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v3 & $i(v3) % 237.30/37.02 | & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 237.30/37.02 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: % 237.30/37.02 | $i] : ( ~ (power_power_int(v5) = v9) | ~ (power_power_int(v4) = % 237.30/37.02 | v6) | ~ (hAPP_i1948725293t_bool(ord_less_int, v7) = v8) | ~ % 237.30/37.02 | (hAPP_nat_int(v9, v2) = v10) | ~ (hAPP_nat_int(v6, v2) = v7) | ~ % 237.30/37.02 | (hAPP_int_bool(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? [v12: % 237.30/37.02 | any] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: % 237.30/37.02 | $i] : ? [v17: any] : (hAPP_i1948725293t_bool(ord_less_int, v4) % 237.30/37.02 | = v15 & hBOOL(v16) = v17 & hBOOL(v13) = v14 & hBOOL(v11) = v12 & % 237.30/37.02 | hAPP_int_bool(v15, v5) = v16 & hAPP_int_bool(v3, v5) = v13 & % 237.30/37.02 | $i(v16) & $i(v15) & $i(v13) & ( ~ (v14 = 0) | ~ (v12 = 0) | v17 % 237.30/37.02 | = 0)))) % 237.30/37.02 | % 237.30/37.02 | ALPHA: (fact_603_sum__power2__ge__zero) implies: % 237.30/37.02 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.30/37.02 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v0 & % 237.30/37.02 | bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/37.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.02 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.02 | ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 237.30/37.02 | (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 237.30/37.02 | (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | % 237.30/37.02 | ~ (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.02 | [v12: $i] : (hBOOL(v12) = 0 & hAPP_real_bool(v0, v11) = v12 & % 237.30/37.02 | $i(v12)))) % 237.30/37.02 | % 237.30/37.02 | ALPHA: (fact_604_sum__power2__ge__zero) implies: % 237.30/37.02 | (101) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(pls) = % 237.30/37.02 | v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.30/37.02 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 237.30/37.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.02 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.30/37.02 | ! [v11: $i] : ( ~ (power_power_int(v5) = v9) | ~ % 237.30/37.02 | (power_power_int(v4) = v6) | ~ (plus_plus_int(v7) = v8) | ~ % 237.30/37.02 | (hAPP_nat_int(v9, v3) = v10) | ~ (hAPP_nat_int(v6, v3) = v7) | % 237.30/37.02 | ~ (hAPP_int_int(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.30/37.02 | [v12: $i] : (hBOOL(v12) = 0 & hAPP_int_bool(v0, v11) = v12 & % 237.30/37.02 | $i(v12)))) % 237.30/37.02 | % 237.30/37.02 | ALPHA: (fact_605_sum__power2__le__zero__iff) implies: % 237.30/37.02 | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) % 237.30/37.02 | = v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 237.30/37.02 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 237.30/37.02 | : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 237.30/37.02 | (plus_plus_real(v6) = v7) | ~ (power_power_real(v4) = v8) | ~ % 237.30/37.02 | (power_power_real(v3) = v5) | ~ (hAPP_nat_real(v8, v2) = v9) | % 237.30/37.02 | ~ (hAPP_nat_real(v5, v2) = v6) | ~ (hAPP_real_real(v7, v9) = % 237.30/37.02 | v10) | ~ $i(v4) | ~ $i(v3) | ? [v11: $i] : ? [v12: $i] : ? % 237.30/37.02 | [v13: int] : ( ~ (v13 = 0) & % 237.30/37.02 | hAPP_r1134773055l_bool(ord_less_eq_real, v10) = v11 & % 237.30/37.02 | hBOOL(v12) = v13 & hAPP_real_bool(v11, zero_zero_real) = v12 & % 237.30/37.02 | $i(v12) & $i(v11)) | (v4 = zero_zero_real & v3 = % 237.30/37.02 | zero_zero_real)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.30/37.02 | [v6: $i] : ( ~ (plus_plus_real(v4) = v5) | ~ % 237.30/37.02 | (power_power_real(zero_zero_real) = v3) | ~ (hAPP_nat_real(v3, % 237.30/37.02 | v2) = v4) | ~ (hAPP_real_real(v5, v4) = v6) | ? [v7: $i] : % 237.30/37.02 | ? [v8: $i] : (hAPP_r1134773055l_bool(ord_less_eq_real, v6) = v7 & % 237.30/37.02 | hBOOL(v8) = 0 & hAPP_real_bool(v7, zero_zero_real) = v8 & % 237.30/37.02 | $i(v8) & $i(v7)))) % 237.30/37.02 | % 237.30/37.02 | ALPHA: (fact_606_sum__power2__le__zero__iff) implies: % 237.56/37.02 | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (bit1(pls) = v0 & bit0(v0) % 237.56/37.02 | = v1 & number_number_of_nat(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 237.56/37.02 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 237.56/37.02 | : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 237.56/37.02 | (power_power_int(v4) = v8) | ~ (power_power_int(v3) = v5) | ~ % 237.56/37.02 | (plus_plus_int(v6) = v7) | ~ (hAPP_nat_int(v8, v2) = v9) | ~ % 237.56/37.02 | (hAPP_nat_int(v5, v2) = v6) | ~ (hAPP_int_int(v7, v9) = v10) | % 237.56/37.02 | ~ $i(v4) | ~ $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: % 237.56/37.02 | int] : ( ~ (v13 = 0) & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.56/37.02 | v10) = v11 & hBOOL(v12) = v13 & hAPP_int_bool(v11, % 237.56/37.02 | zero_zero_int) = v12 & $i(v12) & $i(v11)) | (v4 = % 237.56/37.02 | zero_zero_int & v3 = zero_zero_int)) & ! [v3: $i] : ! [v4: % 237.56/37.02 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.56/37.02 | (power_power_int(zero_zero_int) = v3) | ~ (plus_plus_int(v4) = % 237.56/37.02 | v5) | ~ (hAPP_nat_int(v3, v2) = v4) | ~ (hAPP_int_int(v5, v4) % 237.56/37.02 | = v6) | ? [v7: $i] : ? [v8: $i] : % 237.56/37.02 | (hAPP_i1948725293t_bool(ord_less_eq_int, v6) = v7 & hBOOL(v8) = 0 % 237.56/37.02 | & hAPP_int_bool(v7, zero_zero_int) = v8 & $i(v8) & $i(v7)))) % 237.56/37.02 | % 237.56/37.02 | ALPHA: (fact_607_int__pos__lt__two__imp__zero__or__one) implies: % 237.56/37.02 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.56/37.02 | (number_number_of_int(v2) = v3 & bit1(pls) = v1 & bit0(v1) = v2 & % 237.56/37.02 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & % 237.56/37.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v4 % 237.56/37.02 | = one_one_int | v4 = zero_zero_int | ~ (hAPP_int_bool(v0, v4) = % 237.56/37.02 | v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? % 237.56/37.02 | [v9: any] : (hAPP_i1948725293t_bool(ord_less_int, v4) = v7 & % 237.56/37.02 | hBOOL(v8) = v9 & hBOOL(v5) = v6 & hAPP_int_bool(v7, v3) = v8 & % 237.56/37.02 | $i(v8) & $i(v7) & ( ~ (v9 = 0) | ~ (v6 = 0))))) % 237.56/37.02 | % 237.56/37.02 | ALPHA: (fact_609_number__of2) implies: % 237.56/37.02 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (number_number_of_int(pls) % 237.56/37.02 | = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 % 237.56/37.02 | & hBOOL(v2) = 0 & hAPP_int_bool(v0, v1) = v2 & $i(v2) & $i(v1) & % 237.56/37.02 | $i(v0)) % 237.56/37.02 | % 237.56/37.02 | ALPHA: (fact_642_two__realpow__ge__one) implies: % 237.56/37.02 | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.56/37.02 | (hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = v0 & % 237.56/37.02 | number267125858f_real(v2) = v3 & power_power_real(v3) = v4 & % 237.56/37.02 | bit1(pls) = v1 & bit0(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 237.56/37.02 | & $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_nat_real(v4, v5) = % 237.56/37.02 | v6) | ~ $i(v5) | ? [v7: $i] : (hBOOL(v7) = 0 & % 237.56/37.02 | hAPP_real_bool(v0, v6) = v7 & $i(v7)))) % 237.56/37.02 | % 237.56/37.02 | ALPHA: (fact_645_ex__least__nat__less) implies: % 237.56/37.02 | (107) $i(one_one_nat) % 237.56/37.02 | % 237.56/37.02 | ALPHA: (fact_690_real__sqrt__sum__squares__ge__zero) implies: % 237.56/37.03 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.56/37.03 | (hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = v0 & % 237.56/37.03 | bit1(pls) = v1 & bit0(v1) = v2 & number_number_of_nat(v2) = v3 & % 237.56/37.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! % 237.56/37.03 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 237.56/37.03 | ! [v11: $i] : ( ~ (plus_plus_real(v7) = v8) | ~ % 237.56/37.03 | (power_power_real(v5) = v9) | ~ (power_power_real(v4) = v6) | ~ % 237.56/37.03 | (hAPP_nat_real(v9, v3) = v10) | ~ (hAPP_nat_real(v6, v3) = v7) | % 237.56/37.03 | ~ (hAPP_real_real(v8, v10) = v11) | ~ $i(v5) | ~ $i(v4) | ? % 237.56/37.03 | [v12: $i] : ? [v13: $i] : (sqrt(v11) = v12 & hBOOL(v13) = 0 & % 237.56/37.03 | hAPP_real_bool(v0, v12) = v13 & $i(v13) & $i(v12)))) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (fact_691_zadd__power2) implies: % 237.56/37.03 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 237.56/37.03 | (number_number_of_int(v1) = v3 & bit1(pls) = v0 & bit0(v0) = v1 & % 237.56/37.03 | number_number_of_nat(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 237.56/37.03 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] % 237.56/37.03 | : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! % 237.56/37.03 | [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~ (times_times_int(v9, % 237.56/37.03 | v5) = v10) | ~ (times_times_int(v3, v4) = v9) | ~ % 237.56/37.03 | (power_power_int(v5) = v13) | ~ (power_power_int(v4) = v6) | ~ % 237.56/37.03 | (plus_plus_int(v11) = v12) | ~ (plus_plus_int(v7) = v8) | ~ % 237.56/37.03 | (hAPP_nat_int(v13, v2) = v14) | ~ (hAPP_nat_int(v6, v2) = v7) | % 237.56/37.03 | ~ (hAPP_int_int(v12, v14) = v15) | ~ (hAPP_int_int(v8, v10) = % 237.56/37.03 | v11) | ~ $i(v5) | ~ $i(v4) | ? [v16: $i] : ? [v17: $i] : ? % 237.56/37.03 | [v18: $i] : (power_power_int(v17) = v18 & plus_plus_int(v4) = v16 % 237.56/37.03 | & hAPP_nat_int(v18, v2) = v15 & hAPP_int_int(v16, v5) = v17 & % 237.56/37.03 | $i(v18) & $i(v17) & $i(v16) & $i(v15)))) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (conj_0) implies: % 237.56/37.03 | (110) $i(n) % 237.56/37.03 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 237.56/37.03 | ? [v5: $i] : ? [v6: $i] : (bit1(pls) = v4 & bit0(v4) = v5 & % 237.56/37.03 | number_number_of_nat(v5) = v6 & power_power_int(v2) = v3 & % 237.56/37.03 | plus_plus_int(one_one_int) = v0 & hAPP_nat_int(v3, v6) = % 237.56/37.03 | zero_zero_int & hAPP_nat_int(semiri1621563631at_int, n) = v1 & % 237.56/37.03 | hAPP_int_int(v0, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 237.56/37.03 | $i(v2) & $i(v1) & $i(v0)) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (function-axioms) implies: % 237.56/37.03 | (112) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 237.56/37.03 | : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) % 237.56/37.03 | (113) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 237.56/37.03 | (plus_plus_int(v2) = v1) | ~ (plus_plus_int(v2) = v0)) % 237.56/37.03 | (114) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 237.56/37.03 | (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) = % 237.56/37.03 | v0)) % 237.56/37.03 | (115) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit0(v2) = % 237.56/37.03 | v1) | ~ (bit0(v2) = v0)) % 237.56/37.03 | (116) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit1(v2) = % 237.56/37.03 | v1) | ~ (bit1(v2) = v0)) % 237.56/37.03 | (117) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 237.56/37.03 | (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) = % 237.56/37.03 | v0)) % 237.56/37.03 | (118) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 237.56/37.03 | (plus_plus_nat(v2) = v1) | ~ (plus_plus_nat(v2) = v0)) % 237.56/37.03 | (119) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.56/37.03 | (hAPP_int_int(v3, v2) = v1) | ~ (hAPP_int_int(v3, v2) = v0)) % 237.56/37.03 | (120) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.56/37.03 | (hAPP_nat_int(v3, v2) = v1) | ~ (hAPP_nat_int(v3, v2) = v0)) % 237.56/37.03 | (121) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.56/37.03 | (hAPP_i1948725293t_bool(v3, v2) = v1) | ~ % 237.56/37.03 | (hAPP_i1948725293t_bool(v3, v2) = v0)) % 237.56/37.03 | (122) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.56/37.03 | (hAPP_nat_nat(v3, v2) = v1) | ~ (hAPP_nat_nat(v3, v2) = v0)) % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (46) with fresh symbol all_439_0 gives: % 237.56/37.03 | (123) number_number_of_int(all_439_0) = one_one_int & bit1(pls) = all_439_0 % 237.56/37.03 | & $i(all_439_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (123) implies: % 237.56/37.03 | (124) bit1(pls) = all_439_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (48) with fresh symbol all_441_0 gives: % 237.56/37.03 | (125) number267125858f_real(all_441_0) = one_one_real & bit1(pls) = % 237.56/37.03 | all_441_0 & $i(all_441_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (125) implies: % 237.56/37.03 | (126) bit1(pls) = all_441_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (47) with fresh symbol all_443_0 gives: % 237.56/37.03 | (127) bit1(pls) = all_443_0 & number_number_of_nat(all_443_0) = one_one_nat % 237.56/37.03 | & $i(all_443_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (127) implies: % 237.56/37.03 | (128) bit1(pls) = all_443_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (47) with fresh symbol all_445_0 gives: % 237.56/37.03 | (129) bit1(pls) = all_445_0 & number_number_of_nat(all_445_0) = one_one_nat % 237.56/37.03 | & $i(all_445_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (129) implies: % 237.56/37.03 | (130) bit1(pls) = all_445_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (48) with fresh symbol all_447_0 gives: % 237.56/37.03 | (131) number267125858f_real(all_447_0) = one_one_real & bit1(pls) = % 237.56/37.03 | all_447_0 & $i(all_447_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (131) implies: % 237.56/37.03 | (132) bit1(pls) = all_447_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (48) with fresh symbol all_449_0 gives: % 237.56/37.03 | (133) number267125858f_real(all_449_0) = one_one_real & bit1(pls) = % 237.56/37.03 | all_449_0 & $i(all_449_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (133) implies: % 237.56/37.03 | (134) bit1(pls) = all_449_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (46) with fresh symbol all_451_0 gives: % 237.56/37.03 | (135) number_number_of_int(all_451_0) = one_one_int & bit1(pls) = all_451_0 % 237.56/37.03 | & $i(all_451_0) % 237.56/37.03 | % 237.56/37.03 | ALPHA: (135) implies: % 237.56/37.03 | (136) bit1(pls) = all_451_0 % 237.56/37.03 | % 237.56/37.03 | DELTA: instantiating (46) with fresh symbol all_453_0 gives: % 237.56/37.03 | (137) number_number_of_int(all_453_0) = one_one_int & bit1(pls) = all_453_0 % 237.56/37.03 | & $i(all_453_0) % 237.56/37.03 | % 237.56/37.04 | ALPHA: (137) implies: % 237.56/37.04 | (138) bit1(pls) = all_453_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (47) with fresh symbol all_455_0 gives: % 237.56/37.04 | (139) bit1(pls) = all_455_0 & number_number_of_nat(all_455_0) = one_one_nat % 237.56/37.04 | & $i(all_455_0) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (139) implies: % 237.56/37.04 | (140) bit1(pls) = all_455_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (46) with fresh symbol all_457_0 gives: % 237.56/37.04 | (141) number_number_of_int(all_457_0) = one_one_int & bit1(pls) = all_457_0 % 237.56/37.04 | & $i(all_457_0) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (141) implies: % 237.56/37.04 | (142) bit1(pls) = all_457_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (83) with fresh symbol all_459_0 gives: % 237.56/37.04 | (143) succ(pls) = all_459_0 & bit1(pls) = all_459_0 & $i(all_459_0) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (143) implies: % 237.56/37.04 | (144) bit1(pls) = all_459_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (63) with fresh symbols all_477_0, all_477_1 gives: % 237.56/37.04 | (145) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_477_1 & % 237.56/37.04 | hBOOL(all_477_0) = 0 & hAPP_int_bool(all_477_1, one_one_int) = % 237.56/37.04 | all_477_0 & $i(all_477_0) & $i(all_477_1) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (145) implies: % 237.56/37.04 | (146) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_477_1 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (32) with fresh symbol all_500_0 gives: % 237.56/37.04 | (147) number_number_of_int(pls) = all_500_0 & $i(all_500_0) & ! [v0: $i] : % 237.56/37.04 | ! [v1: $i] : ( ~ (plus_plus_int(v0) = v1) | ~ $i(v0) | % 237.56/37.04 | hAPP_int_int(v1, all_500_0) = v0) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (147) implies: % 237.56/37.04 | (148) $i(all_500_0) % 237.56/37.04 | (149) number_number_of_int(pls) = all_500_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (63) with fresh symbols all_519_0, all_519_1 gives: % 237.56/37.04 | (150) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_519_1 & % 237.56/37.04 | hBOOL(all_519_0) = 0 & hAPP_int_bool(all_519_1, one_one_int) = % 237.56/37.04 | all_519_0 & $i(all_519_0) & $i(all_519_1) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (150) implies: % 237.56/37.04 | (151) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_519_1 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (19) with fresh symbols all_548_0, all_548_1, all_548_2 % 237.56/37.04 | gives: % 237.56/37.04 | (152) ~ (all_548_0 = 0) & hAPP_i1948725293t_bool(ord_less_int, pls) = % 237.56/37.04 | all_548_2 & hBOOL(all_548_1) = all_548_0 & hAPP_int_bool(all_548_2, % 237.56/37.04 | pls) = all_548_1 & $i(all_548_1) & $i(all_548_2) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (152) implies: % 237.56/37.04 | (153) hAPP_i1948725293t_bool(ord_less_int, pls) = all_548_2 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (23) with fresh symbols all_552_0, all_552_1, all_552_2 % 237.56/37.04 | gives: % 237.56/37.04 | (154) ~ (all_552_0 = 0) & hAPP_i1948725293t_bool(ord_less_int, pls) = % 237.56/37.04 | all_552_2 & hBOOL(all_552_1) = all_552_0 & hAPP_int_bool(all_552_2, % 237.56/37.04 | zero_zero_int) = all_552_1 & $i(all_552_1) & $i(all_552_2) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (154) implies: % 237.56/37.04 | (155) hAPP_i1948725293t_bool(ord_less_int, pls) = all_552_2 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (35) with fresh symbol all_563_0 gives: % 237.56/37.04 | (156) plus_plus_int(one_one_int) = all_563_0 & $i(all_563_0) & ! [v0: $i] % 237.56/37.04 | : ! [v1: $i] : ! [v2: $i] : ( ~ (plus_plus_int(v1) = v2) | ~ % 237.56/37.04 | (hAPP_int_int(v2, v0) = zero_zero_int) | ~ % 237.56/37.04 | (hAPP_int_int(all_563_0, v0) = v1) | ~ $i(v0)) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (156) implies: % 237.56/37.04 | (157) plus_plus_int(one_one_int) = all_563_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (105) with fresh symbols all_580_0, all_580_1, all_580_2 % 237.56/37.04 | gives: % 237.56/37.04 | (158) number_number_of_int(pls) = all_580_1 & % 237.56/37.04 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_580_2 & % 237.56/37.04 | hBOOL(all_580_0) = 0 & hAPP_int_bool(all_580_2, all_580_1) = % 237.56/37.04 | all_580_0 & $i(all_580_0) & $i(all_580_1) & $i(all_580_2) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (158) implies: % 237.56/37.04 | (159) number_number_of_int(pls) = all_580_1 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (31) with fresh symbols all_594_0, all_594_1 gives: % 237.56/37.04 | (160) number_number_of_int(pls) = all_594_1 & plus_plus_int(all_594_1) = % 237.56/37.04 | all_594_0 & $i(all_594_0) & $i(all_594_1) & ! [v0: $i] : ! [v1: $i] % 237.56/37.04 | : (v1 = v0 | ~ (hAPP_int_int(all_594_0, v0) = v1) | ~ $i(v0)) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (160) implies: % 237.56/37.04 | (161) number_number_of_int(pls) = all_594_1 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (34) with fresh symbol all_612_0 gives: % 237.56/37.04 | (162) plus_plus_int(one_one_int) = all_612_0 & $i(all_612_0) & ! [v0: $i] % 237.56/37.04 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus_int(v1) = % 237.56/37.04 | v2) | ~ (hAPP_int_int(v2, v0) = v3) | ~ % 237.56/37.04 | (hAPP_int_int(all_612_0, v0) = v1) | ~ $i(v0) | (bit1(v0) = v3 & % 237.56/37.04 | $i(v3))) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (162) implies: % 237.56/37.04 | (163) plus_plus_int(one_one_int) = all_612_0 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (57) with fresh symbols all_621_0, all_621_1, all_621_2, % 237.56/37.04 | all_621_3 gives: % 237.56/37.04 | (164) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_621_3 & % 237.56/37.04 | plus_plus_nat(one_one_nat) = all_621_2 & hAPP_nat_nat(all_621_2, % 237.56/37.04 | one_one_nat) = all_621_1 & hBOOL(all_621_0) = 0 & % 237.56/37.04 | hAPP_nat_bool(all_621_3, all_621_1) = all_621_0 & $i(all_621_0) & % 237.56/37.04 | $i(all_621_1) & $i(all_621_2) & $i(all_621_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (164) implies: % 237.56/37.04 | (165) hAPP_nat_nat(all_621_2, one_one_nat) = all_621_1 % 237.56/37.04 | (166) plus_plus_nat(one_one_nat) = all_621_2 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (56) with fresh symbols all_623_0, all_623_1, all_623_2, % 237.56/37.04 | all_623_3 gives: % 237.56/37.04 | (167) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_623_3 & % 237.56/37.04 | plus_plus_int(one_one_int) = all_623_2 & hAPP_int_int(all_623_2, % 237.56/37.04 | one_one_int) = all_623_1 & hBOOL(all_623_0) = 0 & % 237.56/37.04 | hAPP_int_bool(all_623_3, all_623_1) = all_623_0 & $i(all_623_0) & % 237.56/37.04 | $i(all_623_1) & $i(all_623_2) & $i(all_623_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (167) implies: % 237.56/37.04 | (168) plus_plus_int(one_one_int) = all_623_2 % 237.56/37.04 | (169) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_623_3 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (16) with fresh symbols all_628_0, all_628_1, all_628_2, % 237.56/37.04 | all_628_3 gives: % 237.56/37.04 | (170) number267125858f_real(all_628_0) = all_628_2 & % 237.56/37.04 | plus_plus_real(one_one_real) = all_628_3 & hAPP_real_real(all_628_3, % 237.56/37.04 | one_one_real) = all_628_2 & bit1(pls) = all_628_1 & bit0(all_628_1) % 237.56/37.04 | = all_628_0 & $i(all_628_0) & $i(all_628_1) & $i(all_628_2) & % 237.56/37.04 | $i(all_628_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (170) implies: % 237.56/37.04 | (171) bit0(all_628_1) = all_628_0 % 237.56/37.04 | (172) bit1(pls) = all_628_1 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (53) with fresh symbols all_630_0, all_630_1, all_630_2, % 237.56/37.04 | all_630_3 gives: % 237.56/37.04 | (173) number_number_of_int(all_630_2) = all_630_1 & bit1(all_630_3) = % 237.56/37.04 | all_630_2 & bit1(pls) = all_630_3 & number_number_of_nat(all_630_2) = % 237.56/37.04 | all_630_0 & hAPP_nat_int(semiri1621563631at_int, all_630_0) = % 237.56/37.04 | all_630_1 & $i(all_630_0) & $i(all_630_1) & $i(all_630_2) & % 237.56/37.04 | $i(all_630_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (173) implies: % 237.56/37.04 | (174) bit1(pls) = all_630_3 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (18) with fresh symbols all_632_0, all_632_1, all_632_2, % 237.56/37.04 | all_632_3 gives: % 237.56/37.04 | (175) plus_plus_nat(one_one_nat) = all_632_3 & hAPP_nat_nat(all_632_3, % 237.56/37.04 | one_one_nat) = all_632_2 & bit1(pls) = all_632_1 & bit0(all_632_1) % 237.56/37.04 | = all_632_0 & number_number_of_nat(all_632_0) = all_632_2 & % 237.56/37.04 | $i(all_632_0) & $i(all_632_1) & $i(all_632_2) & $i(all_632_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (175) implies: % 237.56/37.04 | (176) $i(all_632_0) % 237.56/37.04 | (177) number_number_of_nat(all_632_0) = all_632_2 % 237.56/37.04 | (178) bit0(all_632_1) = all_632_0 % 237.56/37.04 | (179) bit1(pls) = all_632_1 % 237.56/37.04 | (180) hAPP_nat_nat(all_632_3, one_one_nat) = all_632_2 % 237.56/37.04 | (181) plus_plus_nat(one_one_nat) = all_632_3 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (18) with fresh symbols all_634_0, all_634_1, all_634_2, % 237.56/37.04 | all_634_3 gives: % 237.56/37.04 | (182) plus_plus_nat(one_one_nat) = all_634_3 & hAPP_nat_nat(all_634_3, % 237.56/37.04 | one_one_nat) = all_634_2 & bit1(pls) = all_634_1 & bit0(all_634_1) % 237.56/37.04 | = all_634_0 & number_number_of_nat(all_634_0) = all_634_2 & % 237.56/37.04 | $i(all_634_0) & $i(all_634_1) & $i(all_634_2) & $i(all_634_3) % 237.56/37.04 | % 237.56/37.04 | ALPHA: (182) implies: % 237.56/37.04 | (183) bit0(all_634_1) = all_634_0 % 237.56/37.04 | (184) bit1(pls) = all_634_1 % 237.56/37.04 | (185) hAPP_nat_nat(all_634_3, one_one_nat) = all_634_2 % 237.56/37.04 | (186) plus_plus_nat(one_one_nat) = all_634_3 % 237.56/37.04 | % 237.56/37.04 | DELTA: instantiating (7) with fresh symbols all_639_0, all_639_1, all_639_2, % 237.56/37.04 | all_639_3 gives: % 237.56/37.05 | (187) power_power_nat(zero_zero_nat) = all_639_3 & hAPP_nat_nat(all_639_3, % 237.56/37.05 | all_639_0) = zero_zero_nat & bit1(pls) = all_639_2 & % 237.56/37.05 | bit0(all_639_2) = all_639_1 & number_number_of_nat(all_639_1) = % 237.56/37.05 | all_639_0 & $i(all_639_0) & $i(all_639_1) & $i(all_639_2) & % 237.56/37.05 | $i(all_639_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (187) implies: % 237.56/37.05 | (188) number_number_of_nat(all_639_1) = all_639_0 % 237.56/37.05 | (189) bit0(all_639_2) = all_639_1 % 237.56/37.05 | (190) bit1(pls) = all_639_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (86) with fresh symbol all_641_0 gives: % 237.56/37.05 | (191) plus_plus_int(one_one_int) = all_641_0 & $i(all_641_0) & ! [v0: $i] % 237.56/37.05 | : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.56/37.05 | [v3: $i] : (number_number_of_int(v1) = v2 & % 237.56/37.05 | number_number_of_int(v0) = v3 & hAPP_int_int(all_641_0, v3) = v2 % 237.56/37.05 | & $i(v3) & $i(v2))) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (191) implies: % 237.56/37.05 | (192) plus_plus_int(one_one_int) = all_641_0 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (4) with fresh symbols all_644_0, all_644_1, all_644_2, % 237.56/37.05 | all_644_3 gives: % 237.56/37.05 | (193) power_power_nat(one_one_nat) = all_644_3 & hAPP_nat_nat(all_644_3, % 237.56/37.05 | all_644_0) = one_one_nat & bit1(pls) = all_644_2 & bit0(all_644_2) % 237.56/37.05 | = all_644_1 & number_number_of_nat(all_644_1) = all_644_0 & % 237.56/37.05 | $i(all_644_0) & $i(all_644_1) & $i(all_644_2) & $i(all_644_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (193) implies: % 237.56/37.05 | (194) number_number_of_nat(all_644_1) = all_644_0 % 237.56/37.05 | (195) bit0(all_644_2) = all_644_1 % 237.56/37.05 | (196) bit1(pls) = all_644_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (6) with fresh symbols all_649_0, all_649_1, all_649_2, % 237.56/37.05 | all_649_3 gives: % 237.56/37.05 | (197) bit1(pls) = all_649_2 & bit0(all_649_2) = all_649_1 & % 237.56/37.05 | number_number_of_nat(all_649_1) = all_649_0 & % 237.56/37.05 | power_power_int(zero_zero_int) = all_649_3 & hAPP_nat_int(all_649_3, % 237.56/37.05 | all_649_0) = zero_zero_int & $i(all_649_0) & $i(all_649_1) & % 237.56/37.05 | $i(all_649_2) & $i(all_649_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (197) implies: % 237.56/37.05 | (198) number_number_of_nat(all_649_1) = all_649_0 % 237.56/37.05 | (199) bit0(all_649_2) = all_649_1 % 237.56/37.05 | (200) bit1(pls) = all_649_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (15) with fresh symbols all_651_0, all_651_1, all_651_2, % 237.56/37.05 | all_651_3 gives: % 237.56/37.05 | (201) number_number_of_int(all_651_0) = all_651_2 & bit1(pls) = all_651_1 & % 237.56/37.05 | bit0(all_651_1) = all_651_0 & plus_plus_int(one_one_int) = all_651_3 % 237.56/37.05 | & hAPP_int_int(all_651_3, one_one_int) = all_651_2 & $i(all_651_0) & % 237.56/37.05 | $i(all_651_1) & $i(all_651_2) & $i(all_651_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (201) implies: % 237.56/37.05 | (202) plus_plus_int(one_one_int) = all_651_3 % 237.56/37.05 | (203) bit0(all_651_1) = all_651_0 % 237.56/37.05 | (204) bit1(pls) = all_651_1 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (16) with fresh symbols all_656_0, all_656_1, all_656_2, % 237.56/37.05 | all_656_3 gives: % 237.56/37.05 | (205) number267125858f_real(all_656_0) = all_656_2 & % 237.56/37.05 | plus_plus_real(one_one_real) = all_656_3 & hAPP_real_real(all_656_3, % 237.56/37.05 | one_one_real) = all_656_2 & bit1(pls) = all_656_1 & bit0(all_656_1) % 237.56/37.05 | = all_656_0 & $i(all_656_0) & $i(all_656_1) & $i(all_656_2) & % 237.56/37.05 | $i(all_656_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (205) implies: % 237.56/37.05 | (206) bit0(all_656_1) = all_656_0 % 237.56/37.05 | (207) bit1(pls) = all_656_1 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (15) with fresh symbols all_658_0, all_658_1, all_658_2, % 237.56/37.05 | all_658_3 gives: % 237.56/37.05 | (208) number_number_of_int(all_658_0) = all_658_2 & bit1(pls) = all_658_1 & % 237.56/37.05 | bit0(all_658_1) = all_658_0 & plus_plus_int(one_one_int) = all_658_3 % 237.56/37.05 | & hAPP_int_int(all_658_3, one_one_int) = all_658_2 & $i(all_658_0) & % 237.56/37.05 | $i(all_658_1) & $i(all_658_2) & $i(all_658_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (208) implies: % 237.56/37.05 | (209) plus_plus_int(one_one_int) = all_658_3 % 237.56/37.05 | (210) bit0(all_658_1) = all_658_0 % 237.56/37.05 | (211) bit1(pls) = all_658_1 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (8) with fresh symbols all_668_0, all_668_1, all_668_2, % 237.56/37.05 | all_668_3 gives: % 237.56/37.05 | (212) power_power_real(zero_zero_real) = all_668_3 & % 237.56/37.05 | hAPP_nat_real(all_668_3, all_668_0) = zero_zero_real & bit1(pls) = % 237.56/37.05 | all_668_2 & bit0(all_668_2) = all_668_1 & % 237.56/37.05 | number_number_of_nat(all_668_1) = all_668_0 & $i(all_668_0) & % 237.56/37.05 | $i(all_668_1) & $i(all_668_2) & $i(all_668_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (212) implies: % 237.56/37.05 | (213) number_number_of_nat(all_668_1) = all_668_0 % 237.56/37.05 | (214) bit0(all_668_2) = all_668_1 % 237.56/37.05 | (215) bit1(pls) = all_668_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (5) with fresh symbols all_670_0, all_670_1, all_670_2, % 237.56/37.05 | all_670_3 gives: % 237.56/37.05 | (216) power_power_real(one_one_real) = all_670_3 & hAPP_nat_real(all_670_3, % 237.56/37.05 | all_670_0) = one_one_real & bit1(pls) = all_670_2 & bit0(all_670_2) % 237.56/37.05 | = all_670_1 & number_number_of_nat(all_670_1) = all_670_0 & % 237.56/37.05 | $i(all_670_0) & $i(all_670_1) & $i(all_670_2) & $i(all_670_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (216) implies: % 237.56/37.05 | (217) number_number_of_nat(all_670_1) = all_670_0 % 237.56/37.05 | (218) bit0(all_670_2) = all_670_1 % 237.56/37.05 | (219) bit1(pls) = all_670_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (52) with fresh symbols all_672_0, all_672_1, all_672_2, % 237.56/37.05 | all_672_3 gives: % 237.56/37.05 | (220) number_number_of_int(all_672_2) = all_672_1 & bit1(pls) = all_672_3 & % 237.56/37.05 | bit0(all_672_3) = all_672_2 & number_number_of_nat(all_672_2) = % 237.56/37.05 | all_672_0 & hAPP_nat_int(semiri1621563631at_int, all_672_0) = % 237.56/37.05 | all_672_1 & $i(all_672_0) & $i(all_672_1) & $i(all_672_2) & % 237.56/37.05 | $i(all_672_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (220) implies: % 237.56/37.05 | (221) number_number_of_nat(all_672_2) = all_672_0 % 237.56/37.05 | (222) bit0(all_672_3) = all_672_2 % 237.56/37.05 | (223) bit1(pls) = all_672_3 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (3) with fresh symbols all_674_0, all_674_1, all_674_2, % 237.56/37.05 | all_674_3 gives: % 237.56/37.05 | (224) bit1(pls) = all_674_2 & bit0(all_674_2) = all_674_1 & % 237.56/37.05 | number_number_of_nat(all_674_1) = all_674_0 & % 237.56/37.05 | power_power_int(one_one_int) = all_674_3 & hAPP_nat_int(all_674_3, % 237.56/37.05 | all_674_0) = one_one_int & $i(all_674_0) & $i(all_674_1) & % 237.56/37.05 | $i(all_674_2) & $i(all_674_3) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (224) implies: % 237.56/37.05 | (225) number_number_of_nat(all_674_1) = all_674_0 % 237.56/37.05 | (226) bit0(all_674_2) = all_674_1 % 237.56/37.05 | (227) bit1(pls) = all_674_2 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (84) with fresh symbols all_676_0, all_676_1, all_676_2, % 237.56/37.05 | all_676_3, all_676_4 gives: % 237.56/37.05 | (228) number_number_of_int(all_676_2) = all_676_1 & bit1(all_676_3) = % 237.56/37.05 | all_676_2 & bit1(pls) = all_676_3 & % 237.56/37.05 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_676_4 & % 237.56/37.05 | hBOOL(all_676_0) = 0 & hAPP_int_bool(all_676_4, all_676_1) = % 237.56/37.05 | all_676_0 & $i(all_676_0) & $i(all_676_1) & $i(all_676_2) & % 237.56/37.05 | $i(all_676_3) & $i(all_676_4) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (228) implies: % 237.56/37.05 | (229) bit1(pls) = all_676_3 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (49) with fresh symbols all_681_0, all_681_1, all_681_2, % 237.56/37.05 | all_681_3, all_681_4 gives: % 237.56/37.05 | (230) hAPP_i1948725293t_bool(ord_less_int, m1) = all_681_4 & % 237.56/37.05 | plus_plus_int(one_one_int) = all_681_3 & % 237.56/37.05 | hAPP_nat_int(semiri1621563631at_int, n) = all_681_2 & % 237.56/37.05 | hAPP_int_int(all_681_3, all_681_2) = all_681_1 & hBOOL(all_681_0) = 0 % 237.56/37.05 | & hAPP_int_bool(all_681_4, all_681_1) = all_681_0 & $i(all_681_0) & % 237.56/37.05 | $i(all_681_1) & $i(all_681_2) & $i(all_681_3) & $i(all_681_4) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (230) implies: % 237.56/37.05 | (231) hAPP_int_int(all_681_3, all_681_2) = all_681_1 % 237.56/37.05 | (232) hAPP_nat_int(semiri1621563631at_int, n) = all_681_2 % 237.56/37.05 | (233) plus_plus_int(one_one_int) = all_681_3 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (87) with fresh symbols all_683_0, all_683_1, all_683_2, % 237.56/37.05 | all_683_3, all_683_4 gives: % 237.56/37.05 | (234) number_number_of_int(all_683_2) = all_683_1 & bit1(pls) = all_683_3 & % 237.56/37.05 | bit0(all_683_3) = all_683_2 & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.56/37.05 | zero_zero_int) = all_683_4 & hBOOL(all_683_0) = 0 & % 237.56/37.05 | hAPP_int_bool(all_683_4, all_683_1) = all_683_0 & $i(all_683_0) & % 237.56/37.05 | $i(all_683_1) & $i(all_683_2) & $i(all_683_3) & $i(all_683_4) % 237.56/37.05 | % 237.56/37.05 | ALPHA: (234) implies: % 237.56/37.05 | (235) bit0(all_683_3) = all_683_2 % 237.56/37.05 | (236) bit1(pls) = all_683_3 % 237.56/37.05 | % 237.56/37.05 | DELTA: instantiating (1) with fresh symbols all_685_0, all_685_1, all_685_2, % 237.56/37.05 | all_685_3, all_685_4 gives: % 237.56/37.06 | (237) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_685_4 & % 237.56/37.06 | plus_plus_int(one_one_int) = all_685_3 & % 237.56/37.06 | hAPP_nat_int(semiri1621563631at_int, n) = all_685_2 & % 237.56/37.06 | hAPP_int_int(all_685_3, all_685_2) = all_685_1 & hBOOL(all_685_0) = 0 % 237.56/37.06 | & hAPP_int_bool(all_685_4, all_685_1) = all_685_0 & $i(all_685_0) & % 237.56/37.06 | $i(all_685_1) & $i(all_685_2) & $i(all_685_3) & $i(all_685_4) % 237.56/37.06 | % 237.56/37.06 | ALPHA: (237) implies: % 237.56/37.06 | (238) $i(all_685_1) % 237.56/37.06 | (239) hAPP_int_bool(all_685_4, all_685_1) = all_685_0 % 237.56/37.06 | (240) hBOOL(all_685_0) = 0 % 237.56/37.06 | (241) hAPP_int_int(all_685_3, all_685_2) = all_685_1 % 237.56/37.06 | (242) hAPP_nat_int(semiri1621563631at_int, n) = all_685_2 % 237.56/37.06 | (243) plus_plus_int(one_one_int) = all_685_3 % 237.56/37.06 | (244) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_685_4 % 237.56/37.06 | % 237.56/37.06 | DELTA: instantiating (65) with fresh symbols all_687_0, all_687_1, all_687_2, % 237.56/37.06 | all_687_3, all_687_4 gives: % 237.56/37.06 | (245) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_687_4 & % 237.56/37.06 | bit1(pls) = all_687_3 & bit0(all_687_3) = all_687_2 & % 237.56/37.06 | number_number_of_nat(all_687_2) = all_687_1 & hBOOL(all_687_0) = 0 & % 237.56/37.06 | hAPP_nat_bool(all_687_4, all_687_1) = all_687_0 & $i(all_687_0) & % 237.56/37.06 | $i(all_687_1) & $i(all_687_2) & $i(all_687_3) & $i(all_687_4) % 237.56/37.06 | % 237.56/37.06 | ALPHA: (245) implies: % 237.56/37.06 | (246) number_number_of_nat(all_687_2) = all_687_1 % 237.56/37.06 | (247) bit0(all_687_3) = all_687_2 % 237.56/37.06 | (248) bit1(pls) = all_687_3 % 237.56/37.06 | % 237.56/37.06 | DELTA: instantiating (45) with fresh symbol all_692_0 gives: % 237.56/37.06 | (249) plus_plus_int(one_one_int) = all_692_0 & $i(all_692_0) & ! [v0: $i] % 237.56/37.06 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 237.56/37.06 | (number_number_of_int(v0) = v1) | ~ (plus_plus_int(v2) = v3) | ~ % 237.56/37.06 | (hAPP_int_int(v3, v1) = v4) | ~ (hAPP_int_int(all_692_0, v1) = v2) % 237.56/37.06 | | ~ $i(v0) | ? [v5: $i] : (number_number_of_int(v5) = v4 & % 237.56/37.06 | bit1(v0) = v5 & $i(v5) & $i(v4))) % 237.56/37.06 | % 237.56/37.06 | ALPHA: (249) implies: % 237.56/37.06 | (250) plus_plus_int(one_one_int) = all_692_0 % 237.56/37.06 | % 237.56/37.06 | DELTA: instantiating (88) with fresh symbols all_698_0, all_698_1, all_698_2 % 237.56/37.06 | gives: % 237.56/37.06 | (251) bit1(pls) = all_698_2 & bit0(all_698_2) = all_698_1 & % 237.56/37.06 | number_number_of_nat(all_698_1) = all_698_0 & $i(all_698_0) & % 237.56/37.06 | $i(all_698_1) & $i(all_698_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.56/37.06 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (power_power_int(v0) = v2) | % 237.56/37.06 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v1) | ~ % 237.56/37.06 | (hAPP_nat_int(v2, all_698_0) = v3) | ~ (hAPP_int_bool(v1, v3) = % 237.56/37.06 | v4) | ~ $i(v0) | hBOOL(v4) = 0) % 237.56/37.06 | % 237.56/37.06 | ALPHA: (251) implies: % 237.56/37.06 | (252) number_number_of_nat(all_698_1) = all_698_0 % 237.56/37.06 | (253) bit0(all_698_2) = all_698_1 % 237.56/37.06 | (254) bit1(pls) = all_698_2 % 237.56/37.06 | % 237.56/37.06 | DELTA: instantiating (13) with fresh symbol all_704_0 gives: % 237.56/37.06 | (255) bit1(pls) = all_704_0 & $i(all_704_0) & ! [v0: $i] : ! [v1: $i] : ( % 237.56/37.06 | ~ (number_number_of_int(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.56/37.06 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (number_number_of_int(v5) = % 237.56/37.06 | v3 & plus_plus_int(v1) = v2 & plus_plus_int(v0) = v4 & % 237.56/37.06 | hAPP_int_int(v4, all_704_0) = v5 & hAPP_int_int(v2, one_one_int) % 237.56/37.06 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 237.56/37.06 | % 237.56/37.06 | ALPHA: (255) implies: % 237.56/37.06 | (256) bit1(pls) = all_704_0 % 237.56/37.06 | % 237.56/37.06 | DELTA: instantiating (66) with fresh symbols all_707_0, all_707_1 gives: % 237.56/37.06 | (257) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_707_0 & % 237.56/37.06 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_707_1 & % 237.56/37.06 | $i(all_707_0) & $i(all_707_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.56/37.06 | (hAPP_int_bool(all_707_1, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.06 | [v3: $i] : (hAPP_nat_int(semiri1621563631at_int, v2) = v0 & % 237.74/37.06 | hBOOL(v3) = 0 & hAPP_nat_bool(all_707_0, v2) = v3 & $i(v3) & % 237.74/37.06 | $i(v2)) | ? [v2: int] : ( ~ (v2 = 0) & hBOOL(v1) = v2)) % 237.74/37.06 | % 237.74/37.06 | ALPHA: (257) implies: % 237.74/37.06 | (258) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_707_1 % 237.74/37.06 | % 237.74/37.06 | DELTA: instantiating (11) with fresh symbols all_710_0, all_710_1, all_710_2 % 237.74/37.06 | gives: % 237.74/37.06 | (259) bit1(pls) = all_710_1 & plus_plus_int(all_710_1) = all_710_0 & % 237.74/37.06 | plus_plus_int(one_one_int) = all_710_2 & $i(all_710_0) & % 237.74/37.06 | $i(all_710_1) & $i(all_710_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.06 | (hAPP_int_int(all_710_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.06 | [v3: $i] : (number_number_of_int(v1) = v3 & % 237.74/37.06 | number_number_of_int(v0) = v2 & hAPP_int_int(all_710_2, v2) = v3 % 237.74/37.06 | & $i(v3) & $i(v2))) % 237.74/37.06 | % 237.74/37.06 | ALPHA: (259) implies: % 237.74/37.06 | (260) plus_plus_int(one_one_int) = all_710_2 % 237.74/37.06 | (261) bit1(pls) = all_710_1 % 237.74/37.06 | % 237.74/37.06 | DELTA: instantiating (12) with fresh symbols all_713_0, all_713_1, all_713_2 % 237.74/37.06 | gives: % 237.74/37.06 | (262) plus_plus_real(one_one_real) = all_713_2 & bit1(pls) = all_713_1 & % 237.74/37.06 | plus_plus_int(all_713_1) = all_713_0 & $i(all_713_0) & $i(all_713_1) % 237.74/37.06 | & $i(all_713_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.06 | (hAPP_int_int(all_713_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.06 | [v3: $i] : (number267125858f_real(v1) = v3 & % 237.74/37.06 | number267125858f_real(v0) = v2 & hAPP_real_real(all_713_2, v2) = % 237.74/37.06 | v3 & $i(v3) & $i(v2))) % 237.74/37.06 | % 237.74/37.06 | ALPHA: (262) implies: % 237.74/37.06 | (263) bit1(pls) = all_713_1 % 237.74/37.06 | % 237.74/37.06 | DELTA: instantiating (14) with fresh symbol all_716_0 gives: % 237.74/37.06 | (264) bit1(pls) = all_716_0 & $i(all_716_0) & ! [v0: $i] : ! [v1: $i] : ( % 237.74/37.06 | ~ (number267125858f_real(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.06 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (number267125858f_real(v5) = % 237.74/37.06 | v3 & plus_plus_real(v1) = v2 & hAPP_real_real(v2, one_one_real) = % 237.74/37.06 | v3 & plus_plus_int(v0) = v4 & hAPP_int_int(v4, all_716_0) = v5 & % 237.74/37.06 | $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 237.74/37.06 | % 237.74/37.06 | ALPHA: (264) implies: % 237.74/37.06 | (265) bit1(pls) = all_716_0 % 237.74/37.06 | % 237.74/37.06 | DELTA: instantiating (10) with fresh symbols all_728_0, all_728_1, all_728_2 % 237.74/37.06 | gives: % 237.74/37.06 | (266) bit1(pls) = all_728_2 & bit0(all_728_2) = all_728_1 & % 237.74/37.06 | number_number_of_nat(all_728_1) = all_728_0 & $i(all_728_0) & % 237.74/37.06 | $i(all_728_1) & $i(all_728_2) & ! [v0: $i] : ! [v1: $i] : (v0 = % 237.74/37.06 | zero_zero_real | ~ (power_power_real(v0) = v1) | ~ $i(v0) | ? % 237.74/37.06 | [v2: $i] : ( ~ (v2 = zero_zero_real) & hAPP_nat_real(v1, all_728_0) % 237.74/37.06 | = v2 & $i(v2))) & ! [v0: $i] : ( ~ % 237.74/37.06 | (power_power_real(zero_zero_real) = v0) | hAPP_nat_real(v0, % 237.74/37.06 | all_728_0) = zero_zero_real) % 237.74/37.06 | % 237.74/37.06 | ALPHA: (266) implies: % 237.74/37.06 | (267) number_number_of_nat(all_728_1) = all_728_0 % 237.74/37.06 | (268) bit0(all_728_2) = all_728_1 % 237.74/37.06 | (269) bit1(pls) = all_728_2 % 237.74/37.06 | % 237.74/37.06 | DELTA: instantiating (64) with fresh symbol all_734_0 gives: % 237.74/37.07 | (270) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_734_0 & % 237.74/37.07 | $i(all_734_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 237.74/37.07 | : ( ~ (power_power_int(v1) = v2) | ~ (hAPP_nat_int(v2, v0) = v3) | % 237.74/37.07 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 237.74/37.07 | ? [v7: any] : (hBOOL(v6) = v7 & hBOOL(v4) = v5 & % 237.74/37.07 | hAPP_int_bool(all_734_0, v3) = v6 & hAPP_int_bool(all_734_0, v1) % 237.74/37.07 | = v4 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | v7 = 0))) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (270) implies: % 237.74/37.07 | (271) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_734_0 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (9) with fresh symbols all_749_0, all_749_1, all_749_2 % 237.74/37.07 | gives: % 237.74/37.07 | (272) bit1(pls) = all_749_2 & bit0(all_749_2) = all_749_1 & % 237.74/37.07 | number_number_of_nat(all_749_1) = all_749_0 & $i(all_749_0) & % 237.74/37.07 | $i(all_749_1) & $i(all_749_2) & ! [v0: $i] : ! [v1: $i] : (v0 = % 237.74/37.07 | zero_zero_int | ~ (power_power_int(v0) = v1) | ~ $i(v0) | ? [v2: % 237.74/37.07 | $i] : ( ~ (v2 = zero_zero_int) & hAPP_nat_int(v1, all_749_0) = v2 % 237.74/37.07 | & $i(v2))) & ! [v0: $i] : ( ~ (power_power_int(zero_zero_int) = % 237.74/37.07 | v0) | hAPP_nat_int(v0, all_749_0) = zero_zero_int) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (272) implies: % 237.74/37.07 | (273) number_number_of_nat(all_749_1) = all_749_0 % 237.74/37.07 | (274) bit0(all_749_2) = all_749_1 % 237.74/37.07 | (275) bit1(pls) = all_749_2 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (50) with fresh symbols all_752_0, all_752_1, all_752_2, % 237.74/37.07 | all_752_3 gives: % 237.74/37.07 | (276) number_number_of_int(all_752_2) = all_752_1 & bit1(pls) = all_752_3 & % 237.74/37.07 | bit0(all_752_3) = all_752_2 & power_power_int(all_752_1) = all_752_0 % 237.74/37.07 | & $i(all_752_0) & $i(all_752_1) & $i(all_752_2) & $i(all_752_3) & ! % 237.74/37.07 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 237.74/37.07 | ~ (hAPP_i1948725293t_bool(ord_less_int, v1) = v2) | ~ % 237.74/37.07 | (hAPP_nat_int(all_752_0, v0) = v3) | ~ % 237.74/37.07 | (hAPP_nat_int(semiri1621563631at_int, v0) = v1) | ~ % 237.74/37.07 | (hAPP_int_bool(v2, v3) = v4) | ~ $i(v0) | hBOOL(v4) = 0) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (276) implies: % 237.74/37.07 | (277) bit0(all_752_3) = all_752_2 % 237.74/37.07 | (278) bit1(pls) = all_752_3 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (51) with fresh symbols all_755_0, all_755_1, all_755_2, % 237.74/37.07 | all_755_3 gives: % 237.74/37.07 | (279) number267125858f_real(all_755_2) = all_755_1 & % 237.74/37.07 | power_power_real(all_755_1) = all_755_0 & bit1(pls) = all_755_3 & % 237.74/37.07 | bit0(all_755_3) = all_755_2 & $i(all_755_0) & $i(all_755_1) & % 237.74/37.07 | $i(all_755_2) & $i(all_755_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.07 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 237.74/37.07 | (hAPP_r1134773055l_bool(ord_less_real, v1) = v2) | ~ % 237.74/37.07 | (hAPP_nat_real(all_755_0, v0) = v3) | ~ % 237.74/37.07 | (hAPP_nat_real(semiri132038758t_real, v0) = v1) | ~ % 237.74/37.07 | (hAPP_real_bool(v2, v3) = v4) | ~ $i(v0) | hBOOL(v4) = 0) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (279) implies: % 237.74/37.07 | (280) bit0(all_755_3) = all_755_2 % 237.74/37.07 | (281) bit1(pls) = all_755_3 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (89) with fresh symbols all_764_0, all_764_1, all_764_2, % 237.74/37.07 | all_764_3 gives: % 237.74/37.07 | (282) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_764_3 % 237.74/37.07 | & bit1(pls) = all_764_2 & bit0(all_764_2) = all_764_1 & % 237.74/37.07 | number_number_of_nat(all_764_1) = all_764_0 & $i(all_764_0) & % 237.74/37.07 | $i(all_764_1) & $i(all_764_2) & $i(all_764_3) & ! [v0: $i] : ! [v1: % 237.74/37.07 | $i] : ( ~ (power_power_real(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 237.74/37.07 | ? [v3: $i] : (hAPP_nat_real(v1, all_764_0) = v2 & hBOOL(v3) = 0 & % 237.74/37.07 | hAPP_real_bool(all_764_3, v2) = v3 & $i(v3) & $i(v2))) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (282) implies: % 237.74/37.07 | (283) number_number_of_nat(all_764_1) = all_764_0 % 237.74/37.07 | (284) bit0(all_764_2) = all_764_1 % 237.74/37.07 | (285) bit1(pls) = all_764_2 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (111) with fresh symbols all_767_0, all_767_1, all_767_2, % 237.74/37.07 | all_767_3, all_767_4, all_767_5, all_767_6 gives: % 237.74/37.07 | (286) bit1(pls) = all_767_2 & bit0(all_767_2) = all_767_1 & % 237.74/37.07 | number_number_of_nat(all_767_1) = all_767_0 & % 237.74/37.07 | power_power_int(all_767_4) = all_767_3 & plus_plus_int(one_one_int) = % 237.74/37.07 | all_767_6 & hAPP_nat_int(all_767_3, all_767_0) = zero_zero_int & % 237.74/37.07 | hAPP_nat_int(semiri1621563631at_int, n) = all_767_5 & % 237.74/37.07 | hAPP_int_int(all_767_6, all_767_5) = all_767_4 & $i(all_767_0) & % 237.74/37.07 | $i(all_767_1) & $i(all_767_2) & $i(all_767_3) & $i(all_767_4) & % 237.74/37.07 | $i(all_767_5) & $i(all_767_6) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (286) implies: % 237.74/37.07 | (287) hAPP_int_int(all_767_6, all_767_5) = all_767_4 % 237.74/37.07 | (288) hAPP_nat_int(semiri1621563631at_int, n) = all_767_5 % 237.74/37.07 | (289) hAPP_nat_int(all_767_3, all_767_0) = zero_zero_int % 237.74/37.07 | (290) plus_plus_int(one_one_int) = all_767_6 % 237.74/37.07 | (291) power_power_int(all_767_4) = all_767_3 % 237.74/37.07 | (292) number_number_of_nat(all_767_1) = all_767_0 % 237.74/37.07 | (293) bit0(all_767_2) = all_767_1 % 237.74/37.07 | (294) bit1(pls) = all_767_2 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (106) with fresh symbols all_769_0, all_769_1, all_769_2, % 237.74/37.07 | all_769_3, all_769_4 gives: % 237.74/37.07 | (295) hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = all_769_4 & % 237.74/37.07 | number267125858f_real(all_769_2) = all_769_1 & % 237.74/37.07 | power_power_real(all_769_1) = all_769_0 & bit1(pls) = all_769_3 & % 237.74/37.07 | bit0(all_769_3) = all_769_2 & $i(all_769_0) & $i(all_769_1) & % 237.74/37.07 | $i(all_769_2) & $i(all_769_3) & $i(all_769_4) & ! [v0: $i] : ! [v1: % 237.74/37.07 | $i] : ( ~ (hAPP_nat_real(all_769_0, v0) = v1) | ~ $i(v0) | ? [v2: % 237.74/37.07 | $i] : (hBOOL(v2) = 0 & hAPP_real_bool(all_769_4, v1) = v2 & % 237.74/37.07 | $i(v2))) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (295) implies: % 237.74/37.07 | (296) bit0(all_769_3) = all_769_2 % 237.74/37.07 | (297) bit1(pls) = all_769_3 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (90) with fresh symbols all_772_0, all_772_1, all_772_2, % 237.74/37.07 | all_772_3 gives: % 237.74/37.07 | (298) bit1(pls) = all_772_2 & bit0(all_772_2) = all_772_1 & % 237.74/37.07 | number_number_of_nat(all_772_1) = all_772_0 & % 237.74/37.07 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_772_3 & % 237.74/37.07 | $i(all_772_0) & $i(all_772_1) & $i(all_772_2) & $i(all_772_3) & ! % 237.74/37.07 | [v0: $i] : ! [v1: $i] : ( ~ (power_power_int(v0) = v1) | ~ $i(v0) | % 237.74/37.07 | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_int(v1, all_772_0) = v2 & % 237.74/37.07 | hBOOL(v3) = 0 & hAPP_int_bool(all_772_3, v2) = v3 & $i(v3) & % 237.74/37.07 | $i(v2))) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (298) implies: % 237.74/37.07 | (299) number_number_of_nat(all_772_1) = all_772_0 % 237.74/37.07 | (300) bit0(all_772_2) = all_772_1 % 237.74/37.07 | (301) bit1(pls) = all_772_2 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (40) with fresh symbols all_775_0, all_775_1, all_775_2 % 237.74/37.07 | gives: % 237.74/37.07 | (302) bit1(pls) = all_775_2 & bit0(all_775_2) = all_775_1 & % 237.74/37.07 | number_number_of_nat(all_775_1) = all_775_0 & $i(all_775_0) & % 237.74/37.07 | $i(all_775_1) & $i(all_775_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.07 | (power_power_real(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 237.74/37.07 | : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 237.74/37.07 | hAPP_r1134773055l_bool(ord_less_real, v2) = v3 & % 237.74/37.07 | hAPP_nat_real(v1, all_775_0) = v2 & hBOOL(v4) = v5 & % 237.74/37.07 | hAPP_real_bool(v3, zero_zero_real) = v4 & $i(v4) & $i(v3) & % 237.74/37.07 | $i(v2))) % 237.74/37.07 | % 237.74/37.07 | ALPHA: (302) implies: % 237.74/37.07 | (303) number_number_of_nat(all_775_1) = all_775_0 % 237.74/37.07 | (304) bit0(all_775_2) = all_775_1 % 237.74/37.07 | (305) bit1(pls) = all_775_2 % 237.74/37.07 | % 237.74/37.07 | DELTA: instantiating (85) with fresh symbols all_778_0, all_778_1, all_778_2 % 237.74/37.07 | gives: % 237.74/37.08 | (306) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_778_2 & % 237.74/37.08 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_778_1 & % 237.74/37.08 | plus_plus_int(one_one_int) = all_778_0 & $i(all_778_0) & % 237.74/37.08 | $i(all_778_1) & $i(all_778_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.08 | (hAPP_int_bool(all_778_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 237.74/37.08 | [v3: $i] : ? [v4: $i] : ? [v5: any] : (hAPP_int_int(all_778_0, % 237.74/37.08 | v0) = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.08 | hAPP_int_bool(all_778_1, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.08 | 0) | v5 = 0))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (306) implies: % 237.74/37.08 | (307) plus_plus_int(one_one_int) = all_778_0 % 237.74/37.08 | (308) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_778_1 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (39) with fresh symbols all_784_0, all_784_1, all_784_2 % 237.74/37.08 | gives: % 237.74/37.08 | (309) bit1(pls) = all_784_2 & bit0(all_784_2) = all_784_1 & % 237.74/37.08 | number_number_of_nat(all_784_1) = all_784_0 & $i(all_784_0) & % 237.74/37.08 | $i(all_784_1) & $i(all_784_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.08 | (power_power_int(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 237.74/37.08 | : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 237.74/37.08 | hAPP_i1948725293t_bool(ord_less_int, v2) = v3 & hAPP_nat_int(v1, % 237.74/37.08 | all_784_0) = v2 & hBOOL(v4) = v5 & hAPP_int_bool(v3, % 237.74/37.08 | zero_zero_int) = v4 & $i(v4) & $i(v3) & $i(v2))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (309) implies: % 237.74/37.08 | (310) number_number_of_nat(all_784_1) = all_784_0 % 237.74/37.08 | (311) bit0(all_784_2) = all_784_1 % 237.74/37.08 | (312) bit1(pls) = all_784_2 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (75) with fresh symbols all_799_0, all_799_1 gives: % 237.74/37.08 | (313) plus_plus_nat(one_one_nat) = all_799_0 & % 237.74/37.08 | hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_799_1 & % 237.74/37.08 | $i(all_799_0) & $i(all_799_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.08 | (hAPP_int_bool(all_799_1, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 237.74/37.08 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (succ(v0) = v5 % 237.74/37.08 | & hAPP_nat_nat(all_799_0, v3) = v4 & number_number_of_nat(v5) = % 237.74/37.08 | v6 & number_number_of_nat(v0) = v3 & hBOOL(v1) = v2 & $i(v6) & % 237.74/37.08 | $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v6 = v4))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (313) implies: % 237.74/37.08 | (314) plus_plus_nat(one_one_nat) = all_799_0 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (76) with fresh symbols all_805_0, all_805_1 gives: % 237.74/37.08 | (315) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_805_1 & % 237.74/37.08 | plus_plus_int(one_one_int) = all_805_0 & $i(all_805_0) & % 237.74/37.08 | $i(all_805_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.08 | (hAPP_int_bool(all_805_1, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 237.74/37.08 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (succ(v0) = v5 % 237.74/37.08 | & number_number_of_int(v5) = v6 & number_number_of_int(v0) = v3 & % 237.74/37.08 | hAPP_int_int(all_805_0, v3) = v4 & hBOOL(v1) = v2 & $i(v6) & % 237.74/37.08 | $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v6 = v4))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (315) implies: % 237.74/37.08 | (316) plus_plus_int(one_one_int) = all_805_0 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (68) with fresh symbol all_835_0 gives: % 237.74/37.08 | (317) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_835_0 & % 237.74/37.08 | $i(all_835_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 237.74/37.08 | : ( ~ (hAPP_int_bool(all_835_0, v1) = v2) | ~ % 237.74/37.08 | (hAPP_int_bool(all_835_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.08 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 237.74/37.08 | : ? [v9: any] : (plus_plus_int(v1) = v6 & hAPP_int_int(v6, v0) = % 237.74/37.08 | v7 & hBOOL(v8) = v9 & hBOOL(v3) = v5 & hBOOL(v2) = v4 & % 237.74/37.08 | hAPP_int_bool(all_835_0, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ( % 237.74/37.08 | ~ (v5 = 0) | ~ (v4 = 0) | v9 = 0))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (317) implies: % 237.74/37.08 | (318) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_835_0 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (101) with fresh symbols all_841_0, all_841_1, all_841_2, % 237.74/37.08 | all_841_3 gives: % 237.74/37.08 | (319) bit1(pls) = all_841_2 & bit0(all_841_2) = all_841_1 & % 237.74/37.08 | number_number_of_nat(all_841_1) = all_841_0 & % 237.74/37.08 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_841_3 & % 237.74/37.08 | $i(all_841_0) & $i(all_841_1) & $i(all_841_2) & $i(all_841_3) & ! % 237.74/37.08 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 237.74/37.08 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(v1) = v5) % 237.74/37.08 | | ~ (power_power_int(v0) = v2) | ~ (plus_plus_int(v3) = v4) | ~ % 237.74/37.08 | (hAPP_nat_int(v5, all_841_0) = v6) | ~ (hAPP_nat_int(v2, % 237.74/37.08 | all_841_0) = v3) | ~ (hAPP_int_int(v4, v6) = v7) | ~ $i(v1) | % 237.74/37.08 | ~ $i(v0) | ? [v8: $i] : (hBOOL(v8) = 0 & hAPP_int_bool(all_841_3, % 237.74/37.08 | v7) = v8 & $i(v8))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (319) implies: % 237.74/37.08 | (320) number_number_of_nat(all_841_1) = all_841_0 % 237.74/37.08 | (321) bit0(all_841_2) = all_841_1 % 237.74/37.08 | (322) bit1(pls) = all_841_2 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (17) with fresh symbols all_844_0, all_844_1, all_844_2, % 237.74/37.08 | all_844_3, all_844_4 gives: % 237.74/37.08 | (323) bit1(pls) = all_844_4 & bit0(all_844_3) = all_844_1 & bit0(all_844_4) % 237.74/37.08 | = all_844_3 & number_number_of_nat(all_844_1) = all_844_0 & % 237.74/37.08 | number_number_of_nat(all_844_3) = all_844_2 & $i(all_844_0) & % 237.74/37.08 | $i(all_844_1) & $i(all_844_2) & $i(all_844_3) & $i(all_844_4) & ! % 237.74/37.08 | [v0: $i] : ! [v1: $i] : ( ~ (power_power_int(v0) = v1) | ~ $i(v0) | % 237.74/37.08 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (power_power_int(v2) = v3 % 237.74/37.08 | & hAPP_nat_int(v3, all_844_2) = v4 & hAPP_nat_int(v1, all_844_0) % 237.74/37.08 | = v4 & hAPP_nat_int(v1, all_844_2) = v2 & $i(v4) & $i(v3) & % 237.74/37.08 | $i(v2))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (323) implies: % 237.74/37.08 | (324) number_number_of_nat(all_844_3) = all_844_2 % 237.74/37.08 | (325) bit0(all_844_4) = all_844_3 % 237.74/37.08 | (326) bit1(pls) = all_844_4 % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (62) with fresh symbol all_856_0 gives: % 237.74/37.08 | (327) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_856_0 & % 237.74/37.08 | $i(all_856_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 237.74/37.08 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.08 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v3) | ~ % 237.74/37.08 | (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, v1) = v5) | ~ % 237.74/37.08 | (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 237.74/37.08 | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: % 237.74/37.08 | any] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & hBOOL(v6) = v11 & % 237.74/37.08 | hAPP_int_bool(v3, v1) = v9 & hAPP_int_bool(all_856_0, v2) = v7 & % 237.74/37.08 | $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v8 = 0) | v11 = 0))) % 237.74/37.08 | % 237.74/37.08 | ALPHA: (327) implies: % 237.74/37.08 | (328) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_856_0 % 237.74/37.08 | (329) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 237.74/37.08 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.08 | v0) = v3) | ~ (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, % 237.74/37.08 | v1) = v5) | ~ (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ % 237.74/37.08 | $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 237.74/37.08 | [v10: any] : ? [v11: any] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & % 237.74/37.08 | hBOOL(v6) = v11 & hAPP_int_bool(v3, v1) = v9 & % 237.74/37.08 | hAPP_int_bool(all_856_0, v2) = v7 & $i(v9) & $i(v7) & ( ~ (v10 = % 237.74/37.08 | 0) | ~ (v8 = 0) | v11 = 0))) % 237.74/37.08 | % 237.74/37.08 | DELTA: instantiating (100) with fresh symbols all_868_0, all_868_1, all_868_2, % 237.74/37.08 | all_868_3 gives: % 237.74/37.09 | (330) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_868_3 % 237.74/37.09 | & bit1(pls) = all_868_2 & bit0(all_868_2) = all_868_1 & % 237.74/37.09 | number_number_of_nat(all_868_1) = all_868_0 & $i(all_868_0) & % 237.74/37.09 | $i(all_868_1) & $i(all_868_2) & $i(all_868_3) & ! [v0: $i] : ! [v1: % 237.74/37.09 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.74/37.09 | [v6: $i] : ! [v7: $i] : ( ~ (plus_plus_real(v3) = v4) | ~ % 237.74/37.09 | (power_power_real(v1) = v5) | ~ (power_power_real(v0) = v2) | ~ % 237.74/37.09 | (hAPP_nat_real(v5, all_868_0) = v6) | ~ (hAPP_nat_real(v2, % 237.74/37.09 | all_868_0) = v3) | ~ (hAPP_real_real(v4, v6) = v7) | ~ $i(v1) % 237.74/37.09 | | ~ $i(v0) | ? [v8: $i] : (hBOOL(v8) = 0 & % 237.74/37.09 | hAPP_real_bool(all_868_3, v7) = v8 & $i(v8))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (330) implies: % 237.74/37.09 | (331) number_number_of_nat(all_868_1) = all_868_0 % 237.74/37.09 | (332) bit0(all_868_2) = all_868_1 % 237.74/37.09 | (333) bit1(pls) = all_868_2 % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (80) with fresh symbol all_880_0 gives: % 237.74/37.09 | (334) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_880_0 & % 237.74/37.09 | $i(all_880_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 237.74/37.09 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.09 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v3) | ~ % 237.74/37.09 | (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, v1) = v5) | ~ % 237.74/37.09 | (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 237.74/37.09 | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: % 237.74/37.09 | any] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & hBOOL(v6) = v11 & % 237.74/37.09 | hAPP_int_bool(v3, v1) = v9 & hAPP_int_bool(all_880_0, v2) = v7 & % 237.74/37.09 | $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v8 = 0) | v11 = 0))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (334) implies: % 237.74/37.09 | (335) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 237.74/37.09 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.09 | v0) = v3) | ~ (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, % 237.74/37.09 | v1) = v5) | ~ (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ % 237.74/37.09 | $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 237.74/37.09 | [v10: any] : ? [v11: any] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & % 237.74/37.09 | hBOOL(v6) = v11 & hAPP_int_bool(v3, v1) = v9 & % 237.74/37.09 | hAPP_int_bool(all_880_0, v2) = v7 & $i(v9) & $i(v7) & ( ~ (v10 = % 237.74/37.09 | 0) | ~ (v8 = 0) | v11 = 0))) % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (104) with fresh symbols all_889_0, all_889_1, all_889_2, % 237.74/37.09 | all_889_3 gives: % 237.74/37.09 | (336) number_number_of_int(all_889_1) = all_889_0 & bit1(pls) = all_889_2 & % 237.74/37.09 | bit0(all_889_2) = all_889_1 & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.74/37.09 | zero_zero_int) = all_889_3 & $i(all_889_0) & $i(all_889_1) & % 237.74/37.09 | $i(all_889_2) & $i(all_889_3) & ! [v0: $i] : ! [v1: $i] : (v0 = % 237.74/37.09 | one_one_int | v0 = zero_zero_int | ~ (hAPP_int_bool(all_889_3, v0) % 237.74/37.09 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? % 237.74/37.09 | [v5: any] : (hAPP_i1948725293t_bool(ord_less_int, v0) = v3 & % 237.74/37.09 | hBOOL(v4) = v5 & hBOOL(v1) = v2 & hAPP_int_bool(v3, all_889_0) = % 237.74/37.09 | v4 & $i(v4) & $i(v3) & ( ~ (v5 = 0) | ~ (v2 = 0)))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (336) implies: % 237.74/37.09 | (337) bit0(all_889_2) = all_889_1 % 237.74/37.09 | (338) bit1(pls) = all_889_2 % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (43) with fresh symbols all_895_0, all_895_1, all_895_2 % 237.74/37.09 | gives: % 237.74/37.09 | (339) bit1(pls) = all_895_2 & bit0(all_895_2) = all_895_1 & % 237.74/37.09 | number_number_of_nat(all_895_1) = all_895_0 & $i(all_895_0) & % 237.74/37.09 | $i(all_895_1) & $i(all_895_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.09 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 237.74/37.09 | [v7: $i] : ( ~ (power_power_int(v1) = v5) | ~ (power_power_int(v0) = % 237.74/37.09 | v2) | ~ (plus_plus_int(v3) = v4) | ~ (hAPP_nat_int(v5, % 237.74/37.09 | all_895_0) = v6) | ~ (hAPP_nat_int(v2, all_895_0) = v3) | ~ % 237.74/37.09 | (hAPP_int_int(v4, v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : % 237.74/37.09 | ? [v9: $i] : ? [v10: int] : ( ~ (v10 = 0) & % 237.74/37.09 | hAPP_i1948725293t_bool(ord_less_int, v7) = v8 & hBOOL(v9) = v10 & % 237.74/37.09 | hAPP_int_bool(v8, zero_zero_int) = v9 & $i(v9) & $i(v8))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (339) implies: % 237.74/37.09 | (340) number_number_of_nat(all_895_1) = all_895_0 % 237.74/37.09 | (341) bit0(all_895_2) = all_895_1 % 237.74/37.09 | (342) bit1(pls) = all_895_2 % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (82) with fresh symbols all_901_0, all_901_1 gives: % 237.74/37.09 | (343) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_901_1 & % 237.74/37.09 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_901_0 & % 237.74/37.09 | $i(all_901_0) & $i(all_901_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.09 | (hAPP_int_bool(all_901_1, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 237.74/37.09 | [v3: $i] : ? [v4: any] : (hBOOL(v3) = v4 & hBOOL(v1) = v2 & % 237.74/37.09 | hAPP_int_bool(all_901_0, v0) = v3 & $i(v3) & ( ~ (v2 = 0) | v4 = % 237.74/37.09 | 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.09 | (hAPP_int_bool(all_901_1, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.09 | [v3: any] : ? [v4: any] : (hBOOL(v2) = v3 & hBOOL(v1) = v4 & % 237.74/37.09 | hAPP_int_bool(all_901_0, v0) = v2 & $i(v2) & ( ~ (v3 = 0) | v4 = % 237.74/37.09 | 0))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (343) implies: % 237.74/37.09 | (344) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_901_0 % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (78) with fresh symbols all_907_0, all_907_1 gives: % 237.74/37.09 | (345) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_907_1 & % 237.74/37.09 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_907_0 & % 237.74/37.09 | $i(all_907_0) & $i(all_907_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.09 | $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(all_907_0, v0) = v3) | ~ % 237.74/37.09 | (hAPP_int_bool(all_907_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.09 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 237.74/37.09 | : ? [v9: any] : (plus_plus_int(v1) = v6 & hAPP_int_int(v6, v0) = % 237.74/37.09 | v7 & hBOOL(v8) = v9 & hBOOL(v3) = v5 & hBOOL(v2) = v4 & % 237.74/37.09 | hAPP_int_bool(all_907_0, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ( % 237.74/37.09 | ~ (v5 = 0) | ~ (v4 = 0) | v9 = 0))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (345) implies: % 237.74/37.09 | (346) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_907_0 % 237.74/37.09 | % 237.74/37.09 | DELTA: instantiating (44) with fresh symbols all_928_0, all_928_1, all_928_2 % 237.74/37.09 | gives: % 237.74/37.09 | (347) bit1(pls) = all_928_2 & bit0(all_928_2) = all_928_1 & % 237.74/37.09 | number_number_of_nat(all_928_1) = all_928_0 & $i(all_928_0) & % 237.74/37.09 | $i(all_928_1) & $i(all_928_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.09 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 237.74/37.09 | [v7: $i] : ( ~ (plus_plus_real(v3) = v4) | ~ (power_power_real(v1) = % 237.74/37.09 | v5) | ~ (power_power_real(v0) = v2) | ~ (hAPP_nat_real(v5, % 237.74/37.09 | all_928_0) = v6) | ~ (hAPP_nat_real(v2, all_928_0) = v3) | ~ % 237.74/37.09 | (hAPP_real_real(v4, v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] % 237.74/37.09 | : ? [v9: $i] : ? [v10: int] : ( ~ (v10 = 0) & % 237.74/37.09 | hAPP_r1134773055l_bool(ord_less_real, v7) = v8 & hBOOL(v9) = v10 % 237.74/37.09 | & hAPP_real_bool(v8, zero_zero_real) = v9 & $i(v9) & $i(v8))) % 237.74/37.09 | % 237.74/37.09 | ALPHA: (347) implies: % 237.74/37.10 | (348) number_number_of_nat(all_928_1) = all_928_0 % 237.74/37.10 | (349) bit0(all_928_2) = all_928_1 % 237.74/37.10 | (350) bit1(pls) = all_928_2 % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (77) with fresh symbols all_931_0, all_931_1 gives: % 237.74/37.10 | (351) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_931_0 & % 237.74/37.10 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_931_1 & % 237.74/37.10 | $i(all_931_0) & $i(all_931_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.10 | $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(all_931_0, v0) = v3) | ~ % 237.74/37.10 | (hAPP_int_bool(all_931_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.10 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 237.74/37.10 | : ? [v9: any] : (plus_plus_int(v1) = v6 & hAPP_int_int(v6, v0) = % 237.74/37.10 | v7 & hBOOL(v8) = v9 & hBOOL(v3) = v5 & hBOOL(v2) = v4 & % 237.74/37.10 | hAPP_int_bool(all_931_1, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ( % 237.74/37.10 | ~ (v5 = 0) | ~ (v4 = 0) | v9 = 0))) % 237.74/37.10 | % 237.74/37.10 | ALPHA: (351) implies: % 237.74/37.10 | (352) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_931_1 % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (54) with fresh symbols all_937_0, all_937_1, all_937_2 % 237.74/37.10 | gives: % 237.74/37.10 | (353) bit1(pls) = all_937_2 & bit0(all_937_2) = all_937_1 & % 237.74/37.10 | number_number_of_nat(all_937_1) = all_937_0 & $i(all_937_0) & % 237.74/37.10 | $i(all_937_1) & $i(all_937_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.10 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.10 | (plus_plus_real(v3) = v4) | ~ (power_power_real(v1) = v5) | ~ % 237.74/37.10 | (power_power_real(v0) = v2) | ~ (hAPP_nat_real(v5, all_937_0) = % 237.74/37.10 | v6) | ~ (hAPP_nat_real(v2, all_937_0) = v3) | ~ % 237.74/37.10 | (hAPP_real_real(v4, v6) = zero_zero_real) | ~ $i(v1) | ~ $i(v0) | % 237.74/37.10 | (v1 = zero_zero_real & v0 = zero_zero_real)) & ! [v0: $i] : ! % 237.74/37.10 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = zero_zero_real | ~ % 237.74/37.10 | (plus_plus_real(v1) = v2) | ~ (power_power_real(zero_zero_real) = % 237.74/37.10 | v0) | ~ (hAPP_nat_real(v0, all_937_0) = v1) | ~ % 237.74/37.10 | (hAPP_real_real(v2, v1) = v3)) % 237.74/37.10 | % 237.74/37.10 | ALPHA: (353) implies: % 237.74/37.10 | (354) number_number_of_nat(all_937_1) = all_937_0 % 237.74/37.10 | (355) bit0(all_937_2) = all_937_1 % 237.74/37.10 | (356) bit1(pls) = all_937_2 % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (2) with fresh symbols all_940_0, all_940_1, all_940_2 % 237.74/37.10 | gives: % 237.74/37.10 | (357) bit1(pls) = all_940_2 & bit0(all_940_2) = all_940_1 & % 237.74/37.10 | number_number_of_nat(all_940_1) = all_940_0 & $i(all_940_0) & % 237.74/37.10 | $i(all_940_1) & $i(all_940_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.10 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.10 | (power_power_int(v1) = v5) | ~ (power_power_int(v0) = v2) | ~ % 237.74/37.10 | (plus_plus_int(v3) = v4) | ~ (hAPP_nat_int(v5, all_940_0) = v6) | % 237.74/37.10 | ~ (hAPP_nat_int(v2, all_940_0) = v3) | ~ (hAPP_int_int(v4, v6) = % 237.74/37.10 | zero_zero_int) | ~ $i(v1) | ~ $i(v0) | (v1 = zero_zero_int & v0 % 237.74/37.10 | = zero_zero_int)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 237.74/37.10 | [v3: $i] : (v3 = zero_zero_int | ~ (power_power_int(zero_zero_int) = % 237.74/37.10 | v0) | ~ (plus_plus_int(v1) = v2) | ~ (hAPP_nat_int(v0, % 237.74/37.10 | all_940_0) = v1) | ~ (hAPP_int_int(v2, v1) = v3)) % 237.74/37.10 | % 237.74/37.10 | ALPHA: (357) implies: % 237.74/37.10 | (358) number_number_of_nat(all_940_1) = all_940_0 % 237.74/37.10 | (359) bit0(all_940_2) = all_940_1 % 237.74/37.10 | (360) bit1(pls) = all_940_2 % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (54) with fresh symbols all_943_0, all_943_1, all_943_2 % 237.74/37.10 | gives: % 237.74/37.10 | (361) bit1(pls) = all_943_2 & bit0(all_943_2) = all_943_1 & % 237.74/37.10 | number_number_of_nat(all_943_1) = all_943_0 & $i(all_943_0) & % 237.74/37.10 | $i(all_943_1) & $i(all_943_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 237.74/37.10 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.10 | (plus_plus_real(v3) = v4) | ~ (power_power_real(v1) = v5) | ~ % 237.74/37.10 | (power_power_real(v0) = v2) | ~ (hAPP_nat_real(v5, all_943_0) = % 237.74/37.10 | v6) | ~ (hAPP_nat_real(v2, all_943_0) = v3) | ~ % 237.74/37.10 | (hAPP_real_real(v4, v6) = zero_zero_real) | ~ $i(v1) | ~ $i(v0) | % 237.74/37.10 | (v1 = zero_zero_real & v0 = zero_zero_real)) & ! [v0: $i] : ! % 237.74/37.10 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = zero_zero_real | ~ % 237.74/37.10 | (plus_plus_real(v1) = v2) | ~ (power_power_real(zero_zero_real) = % 237.74/37.10 | v0) | ~ (hAPP_nat_real(v0, all_943_0) = v1) | ~ % 237.74/37.10 | (hAPP_real_real(v2, v1) = v3)) % 237.74/37.10 | % 237.74/37.10 | ALPHA: (361) implies: % 237.74/37.10 | (362) number_number_of_nat(all_943_1) = all_943_0 % 237.74/37.10 | (363) bit0(all_943_2) = all_943_1 % 237.74/37.10 | (364) bit1(pls) = all_943_2 % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (79) with fresh symbol all_946_0 gives: % 237.74/37.10 | (365) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_946_0 & % 237.74/37.10 | $i(all_946_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 237.74/37.10 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 237.74/37.10 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v3) | ~ % 237.74/37.10 | (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, v1) = v5) | ~ % 237.74/37.10 | (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 237.74/37.10 | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 237.74/37.10 | any] : ? [v12: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 237.74/37.10 | v0) = v9 & hBOOL(v10) = v11 & hBOOL(v7) = v8 & hBOOL(v6) = v12 % 237.74/37.10 | & hAPP_int_bool(v9, v1) = v10 & hAPP_int_bool(all_946_0, v2) = v7 % 237.74/37.10 | & $i(v10) & $i(v9) & $i(v7) & ( ~ (v11 = 0) | ~ (v8 = 0) | v12 = % 237.74/37.10 | 0))) % 237.74/37.10 | % 237.74/37.10 | ALPHA: (365) implies: % 237.74/37.10 | (366) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_946_0 % 237.74/37.10 | (367) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 237.74/37.10 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.10 | v0) = v3) | ~ (plus_plus_int(v2) = v4) | ~ (hAPP_int_int(v4, % 237.74/37.10 | v1) = v5) | ~ (hAPP_int_bool(v3, v5) = v6) | ~ $i(v2) | ~ % 237.74/37.10 | $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 237.74/37.10 | [v10: $i] : ? [v11: any] : ? [v12: any] : % 237.74/37.10 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v9 & hBOOL(v10) = % 237.74/37.10 | v11 & hBOOL(v7) = v8 & hBOOL(v6) = v12 & hAPP_int_bool(v9, v1) = % 237.74/37.10 | v10 & hAPP_int_bool(all_946_0, v2) = v7 & $i(v10) & $i(v9) & % 237.74/37.10 | $i(v7) & ( ~ (v11 = 0) | ~ (v8 = 0) | v12 = 0))) % 237.74/37.10 | % 237.74/37.10 | DELTA: instantiating (108) with fresh symbols all_952_0, all_952_1, all_952_2, % 237.74/37.10 | all_952_3 gives: % 237.74/37.10 | (368) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_952_3 % 237.74/37.10 | & bit1(pls) = all_952_2 & bit0(all_952_2) = all_952_1 & % 237.74/37.10 | number_number_of_nat(all_952_1) = all_952_0 & $i(all_952_0) & % 237.74/37.10 | $i(all_952_1) & $i(all_952_2) & $i(all_952_3) & ! [v0: $i] : ! [v1: % 237.74/37.10 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.74/37.10 | [v6: $i] : ! [v7: $i] : ( ~ (plus_plus_real(v3) = v4) | ~ % 237.74/37.10 | (power_power_real(v1) = v5) | ~ (power_power_real(v0) = v2) | ~ % 237.74/37.11 | (hAPP_nat_real(v5, all_952_0) = v6) | ~ (hAPP_nat_real(v2, % 237.74/37.11 | all_952_0) = v3) | ~ (hAPP_real_real(v4, v6) = v7) | ~ $i(v1) % 237.74/37.11 | | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : (sqrt(v7) = v8 & % 237.74/37.11 | hBOOL(v9) = 0 & hAPP_real_bool(all_952_3, v8) = v9 & $i(v9) & % 237.74/37.11 | $i(v8))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (368) implies: % 237.74/37.11 | (369) number_number_of_nat(all_952_1) = all_952_0 % 237.74/37.11 | (370) bit0(all_952_2) = all_952_1 % 237.74/37.11 | (371) bit1(pls) = all_952_2 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (22) with fresh symbol all_961_0 gives: % 237.74/37.11 | (372) hAPP_i1948725293t_bool(ord_less_int, pls) = all_961_0 & $i(all_961_0) % 237.74/37.11 | & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_int_bool(all_961_0, v0) = v1) % 237.74/37.11 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 237.74/37.11 | any] : (bit0(v0) = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.11 | hAPP_int_bool(all_961_0, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.11 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.11 | (hAPP_int_bool(all_961_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.11 | [v3: $i] : ? [v4: any] : ? [v5: any] : (bit0(v0) = v2 & hBOOL(v3) % 237.74/37.11 | = v4 & hBOOL(v1) = v5 & hAPP_int_bool(all_961_0, v2) = v3 & % 237.74/37.11 | $i(v3) & $i(v2) & ( ~ (v4 = 0) | v5 = 0))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (372) implies: % 237.74/37.11 | (373) hAPP_i1948725293t_bool(ord_less_int, pls) = all_961_0 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (38) with fresh symbols all_1018_0, all_1018_1, % 237.74/37.11 | all_1018_2, all_1018_3 gives: % 237.74/37.11 | (374) hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = all_1018_3 & % 237.74/37.11 | bit1(pls) = all_1018_2 & bit0(all_1018_2) = all_1018_1 & % 237.74/37.11 | number_number_of_nat(all_1018_1) = all_1018_0 & $i(all_1018_0) & % 237.74/37.11 | $i(all_1018_1) & $i(all_1018_2) & $i(all_1018_3) & ! [v0: $i] : ! % 237.74/37.11 | [v1: $i] : (v0 = zero_zero_real | ~ (power_power_real(v0) = v1) | ~ % 237.74/37.11 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_real(v1, all_1018_0) % 237.74/37.11 | = v2 & hBOOL(v3) = 0 & hAPP_real_bool(all_1018_3, v2) = v3 & % 237.74/37.11 | $i(v3) & $i(v2))) & ! [v0: $i] : ( ~ % 237.74/37.11 | (power_power_real(zero_zero_real) = v0) | ? [v1: $i] : ? [v2: $i] % 237.74/37.11 | : ? [v3: int] : ( ~ (v3 = 0) & hAPP_nat_real(v0, all_1018_0) = v1 % 237.74/37.11 | & hBOOL(v2) = v3 & hAPP_real_bool(all_1018_3, v1) = v2 & $i(v2) & % 237.74/37.11 | $i(v1))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (374) implies: % 237.74/37.11 | (375) number_number_of_nat(all_1018_1) = all_1018_0 % 237.74/37.11 | (376) bit0(all_1018_2) = all_1018_1 % 237.74/37.11 | (377) bit1(pls) = all_1018_2 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (37) with fresh symbols all_1036_0, all_1036_1, % 237.74/37.11 | all_1036_2, all_1036_3 gives: % 237.74/37.11 | (378) bit1(pls) = all_1036_2 & bit0(all_1036_2) = all_1036_1 & % 237.74/37.11 | number_number_of_nat(all_1036_1) = all_1036_0 & % 237.74/37.11 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1036_3 & % 237.74/37.11 | $i(all_1036_0) & $i(all_1036_1) & $i(all_1036_2) & $i(all_1036_3) & % 237.74/37.11 | ! [v0: $i] : ! [v1: $i] : (v0 = zero_zero_int | ~ % 237.74/37.11 | (power_power_int(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] % 237.74/37.11 | : (hAPP_nat_int(v1, all_1036_0) = v2 & hBOOL(v3) = 0 & % 237.74/37.11 | hAPP_int_bool(all_1036_3, v2) = v3 & $i(v3) & $i(v2))) & ! [v0: % 237.74/37.11 | $i] : ( ~ (power_power_int(zero_zero_int) = v0) | ? [v1: $i] : ? % 237.74/37.11 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & hAPP_nat_int(v0, % 237.74/37.11 | all_1036_0) = v1 & hBOOL(v2) = v3 & hAPP_int_bool(all_1036_3, % 237.74/37.11 | v1) = v2 & $i(v2) & $i(v1))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (378) implies: % 237.74/37.11 | (379) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1036_3 % 237.74/37.11 | (380) number_number_of_nat(all_1036_1) = all_1036_0 % 237.74/37.11 | (381) bit0(all_1036_2) = all_1036_1 % 237.74/37.11 | (382) bit1(pls) = all_1036_2 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (60) with fresh symbols all_1051_0, all_1051_1 gives: % 237.74/37.11 | (383) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1051_0 & % 237.74/37.11 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1051_1 & % 237.74/37.11 | $i(all_1051_0) & $i(all_1051_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.11 | (hAPP_nat_bool(all_1051_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.11 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 237.74/37.11 | (hAPP_nat_int(semiri1621563631at_int, v0) = v3 & hBOOL(v4) = v5 & % 237.74/37.11 | hBOOL(v1) = v2 & hAPP_int_bool(all_1051_1, v3) = v4 & $i(v4) & % 237.74/37.11 | $i(v3) & ( ~ (v2 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 237.74/37.11 | ~ (hAPP_nat_bool(all_1051_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 237.74/37.11 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 237.74/37.11 | (hAPP_nat_int(semiri1621563631at_int, v0) = v2 & hBOOL(v3) = v4 & % 237.74/37.11 | hBOOL(v1) = v5 & hAPP_int_bool(all_1051_1, v2) = v3 & $i(v3) & % 237.74/37.11 | $i(v2) & ( ~ (v4 = 0) | v5 = 0))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (383) implies: % 237.74/37.11 | (384) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1051_1 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (21) with fresh symbols all_1054_0, all_1054_1 gives: % 237.74/37.11 | (385) hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = all_1054_1 & % 237.74/37.11 | hAPP_i1948725293t_bool(ord_less_int, pls) = all_1054_0 & % 237.74/37.11 | $i(all_1054_0) & $i(all_1054_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.11 | (hAPP_int_bool(all_1054_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.11 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 237.74/37.11 | (number267125858f_real(v0) = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.11 | hAPP_real_bool(all_1054_1, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.11 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.11 | (hAPP_int_bool(all_1054_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.11 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number267125858f_real(v0) % 237.74/37.11 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.11 | hAPP_real_bool(all_1054_1, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.11 | 0) | v5 = 0))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (385) implies: % 237.74/37.11 | (386) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1054_0 % 237.74/37.11 | % 237.74/37.11 | DELTA: instantiating (60) with fresh symbols all_1066_0, all_1066_1 gives: % 237.74/37.11 | (387) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1066_0 & % 237.74/37.11 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1066_1 & % 237.74/37.11 | $i(all_1066_0) & $i(all_1066_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.11 | (hAPP_nat_bool(all_1066_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.11 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 237.74/37.11 | (hAPP_nat_int(semiri1621563631at_int, v0) = v3 & hBOOL(v4) = v5 & % 237.74/37.11 | hBOOL(v1) = v2 & hAPP_int_bool(all_1066_1, v3) = v4 & $i(v4) & % 237.74/37.11 | $i(v3) & ( ~ (v2 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 237.74/37.11 | ~ (hAPP_nat_bool(all_1066_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 237.74/37.11 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 237.74/37.11 | (hAPP_nat_int(semiri1621563631at_int, v0) = v2 & hBOOL(v3) = v4 & % 237.74/37.11 | hBOOL(v1) = v5 & hAPP_int_bool(all_1066_1, v2) = v3 & $i(v3) & % 237.74/37.11 | $i(v2) & ( ~ (v4 = 0) | v5 = 0))) % 237.74/37.11 | % 237.74/37.11 | ALPHA: (387) implies: % 237.74/37.12 | (388) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1066_1 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (20) with fresh symbols all_1072_0, all_1072_1 gives: % 237.74/37.12 | (389) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1072_0 & % 237.74/37.12 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1072_1 & % 237.74/37.12 | $i(all_1072_0) & $i(all_1072_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1072_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.12 | = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.12 | hAPP_int_bool(all_1072_1, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.12 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1072_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.12 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.12 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.12 | hAPP_int_bool(all_1072_1, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.12 | 0) | v5 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (389) implies: % 237.74/37.12 | (390) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1072_1 % 237.74/37.12 | (391) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1072_0 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (81) with fresh symbols all_1078_0, all_1078_1 gives: % 237.74/37.12 | (392) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1078_0 & % 237.74/37.12 | hAPP_i1948725293t_bool(ord_less_int, pls) = all_1078_1 & % 237.74/37.12 | $i(all_1078_0) & $i(all_1078_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1078_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (bit1(v0) = v3 & % 237.74/37.12 | hBOOL(v4) = v5 & hBOOL(v1) = v2 & hAPP_int_bool(all_1078_1, v3) = % 237.74/37.12 | v4 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = 0))) & ! [v0: $i] : % 237.74/37.12 | ! [v1: $i] : ( ~ (hAPP_int_bool(all_1078_0, v0) = v1) | ~ $i(v0) | % 237.74/37.12 | ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: any] : (bit1(v0) % 237.74/37.12 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.12 | hAPP_int_bool(all_1078_1, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.12 | 0) | v5 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (392) implies: % 237.74/37.12 | (393) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1078_1 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (59) with fresh symbols all_1081_0, all_1081_1 gives: % 237.74/37.12 | (394) hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1081_1 & % 237.74/37.12 | hAPP_i1948725293t_bool(ord_less_int, pls) = all_1081_0 & % 237.74/37.12 | $i(all_1081_0) & $i(all_1081_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1081_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (number_number_of_nat(v0) % 237.74/37.12 | = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.12 | hAPP_nat_bool(all_1081_1, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.12 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1081_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.12 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number_number_of_nat(v0) % 237.74/37.12 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.12 | hAPP_nat_bool(all_1081_1, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.12 | 0) | v5 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (394) implies: % 237.74/37.12 | (395) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1081_0 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (67) with fresh symbol all_1099_0 gives: % 237.74/37.12 | (396) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1099_0 & % 237.74/37.12 | $i(all_1099_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1099_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : % 237.74/37.12 | (plus_plus_int(v0) = v3 & hAPP_int_int(v3, v0) = v4 & hBOOL(v5) = % 237.74/37.12 | v6 & hBOOL(v1) = v2 & hAPP_int_bool(all_1099_0, v4) = v5 & $i(v5) % 237.74/37.12 | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v6 = 0))) & ! [v0: $i] : ! % 237.74/37.12 | [v1: $i] : ( ~ (hAPP_int_bool(all_1099_0, v0) = v1) | ~ $i(v0) | ? % 237.74/37.12 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any] % 237.74/37.12 | : (plus_plus_int(v0) = v2 & hAPP_int_int(v2, v0) = v3 & hBOOL(v4) = % 237.74/37.12 | v5 & hBOOL(v1) = v6 & hAPP_int_bool(all_1099_0, v3) = v4 & $i(v4) % 237.74/37.12 | & $i(v3) & $i(v2) & ( ~ (v5 = 0) | v6 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (396) implies: % 237.74/37.12 | (397) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1099_0 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (95) with fresh symbols all_1102_0, all_1102_1, % 237.74/37.12 | all_1102_2, all_1102_3 gives: % 237.74/37.12 | (398) hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = all_1102_0 & % 237.74/37.12 | bit1(pls) = all_1102_3 & bit0(all_1102_3) = all_1102_2 & % 237.74/37.12 | number_number_of_nat(all_1102_2) = all_1102_1 & $i(all_1102_0) & % 237.74/37.12 | $i(all_1102_1) & $i(all_1102_2) & $i(all_1102_3) & ! [v0: $i] : ! % 237.74/37.12 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.74/37.12 | (hAPP_nat_bool(all_1102_0, v1) = v3) | ~ % 237.74/37.12 | (hAPP_nat_bool(all_1102_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.12 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 237.74/37.12 | ? [v9: any] : (power_power_nat(v1) = v6 & power_power_nat(v0) = v4 % 237.74/37.12 | & hAPP_nat_nat(v6, all_1102_1) = v7 & hAPP_nat_nat(v4, % 237.74/37.12 | all_1102_1) = v5 & hBOOL(v3) = v9 & hBOOL(v2) = v8 & $i(v7) & % 237.74/37.12 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = % 237.74/37.12 | v5)))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (398) implies: % 237.74/37.12 | (399) number_number_of_nat(all_1102_2) = all_1102_1 % 237.74/37.12 | (400) bit0(all_1102_3) = all_1102_2 % 237.74/37.12 | (401) bit1(pls) = all_1102_3 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (27) with fresh symbols all_1105_0, all_1105_1, % 237.74/37.12 | all_1105_2 gives: % 237.74/37.12 | (402) hAPP_r1134773055l_bool(ord_less_real, one_one_real) = all_1105_2 & % 237.74/37.12 | bit1(pls) = all_1105_1 & hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.12 | all_1105_1) = all_1105_0 & $i(all_1105_0) & $i(all_1105_1) & % 237.74/37.12 | $i(all_1105_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1105_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 237.74/37.12 | (number267125858f_real(v0) = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.12 | hAPP_real_bool(all_1105_2, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.12 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1105_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.12 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number267125858f_real(v0) % 237.74/37.12 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.12 | hAPP_real_bool(all_1105_2, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.12 | 0) | v5 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (402) implies: % 237.74/37.12 | (403) bit1(pls) = all_1105_1 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (26) with fresh symbols all_1111_0, all_1111_1, % 237.74/37.12 | all_1111_2 gives: % 237.74/37.12 | (404) bit1(pls) = all_1111_1 & hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.12 | all_1111_1) = all_1111_0 & hAPP_i1948725293t_bool(ord_less_int, % 237.74/37.12 | one_one_int) = all_1111_2 & $i(all_1111_0) & $i(all_1111_1) & % 237.74/37.12 | $i(all_1111_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1111_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.12 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.12 | = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.12 | hAPP_int_bool(all_1111_2, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.12 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.12 | (hAPP_int_bool(all_1111_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.12 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.12 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.12 | hAPP_int_bool(all_1111_2, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.12 | 0) | v5 = 0))) % 237.74/37.12 | % 237.74/37.12 | ALPHA: (404) implies: % 237.74/37.12 | (405) bit1(pls) = all_1111_1 % 237.74/37.12 | % 237.74/37.12 | DELTA: instantiating (71) with fresh symbols all_1123_0, all_1123_1, % 237.74/37.12 | all_1123_2 gives: % 237.74/37.13 | (406) hAPP_r1134773055l_bool(ord_less_eq_real, one_one_real) = all_1123_2 & % 237.74/37.13 | bit1(pls) = all_1123_1 & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.74/37.13 | all_1123_1) = all_1123_0 & $i(all_1123_0) & $i(all_1123_1) & % 237.74/37.13 | $i(all_1123_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.13 | (hAPP_int_bool(all_1123_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.13 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 237.74/37.13 | (number267125858f_real(v0) = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.13 | hAPP_real_bool(all_1123_2, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.13 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.13 | (hAPP_int_bool(all_1123_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.13 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number267125858f_real(v0) % 237.74/37.13 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.13 | hAPP_real_bool(all_1123_2, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.13 | 0) | v5 = 0))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (406) implies: % 237.74/37.13 | (407) bit1(pls) = all_1123_1 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (72) with fresh symbols all_1132_0, all_1132_1, % 237.74/37.13 | all_1132_2 gives: % 237.74/37.13 | (408) bit1(pls) = all_1132_1 & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.74/37.13 | all_1132_1) = all_1132_0 & hAPP_i1948725293t_bool(ord_less_eq_int, % 237.74/37.13 | one_one_int) = all_1132_2 & $i(all_1132_0) & $i(all_1132_1) & % 237.74/37.13 | $i(all_1132_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.13 | (hAPP_int_bool(all_1132_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 237.74/37.13 | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.13 | = v3 & hBOOL(v4) = v5 & hBOOL(v1) = v2 & % 237.74/37.13 | hAPP_int_bool(all_1132_2, v3) = v4 & $i(v4) & $i(v3) & ( ~ (v2 = % 237.74/37.13 | 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 237.74/37.13 | (hAPP_int_bool(all_1132_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 237.74/37.13 | [v3: $i] : ? [v4: any] : ? [v5: any] : (number_number_of_int(v0) % 237.74/37.13 | = v2 & hBOOL(v3) = v4 & hBOOL(v1) = v5 & % 237.74/37.13 | hAPP_int_bool(all_1132_2, v2) = v3 & $i(v3) & $i(v2) & ( ~ (v4 = % 237.74/37.13 | 0) | v5 = 0))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (408) implies: % 237.74/37.13 | (409) bit1(pls) = all_1132_1 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (94) with fresh symbols all_1135_0, all_1135_1, % 237.74/37.13 | all_1135_2, all_1135_3 gives: % 237.74/37.13 | (410) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_1135_0 % 237.74/37.13 | & bit1(pls) = all_1135_3 & bit0(all_1135_3) = all_1135_2 & % 237.74/37.13 | number_number_of_nat(all_1135_2) = all_1135_1 & $i(all_1135_0) & % 237.74/37.13 | $i(all_1135_1) & $i(all_1135_2) & $i(all_1135_3) & ! [v0: $i] : ! % 237.74/37.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.74/37.13 | (hAPP_real_bool(all_1135_0, v1) = v3) | ~ % 237.74/37.13 | (hAPP_real_bool(all_1135_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.13 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 237.74/37.13 | ? [v9: any] : (power_power_real(v1) = v6 & power_power_real(v0) = % 237.74/37.13 | v4 & hAPP_nat_real(v6, all_1135_1) = v7 & hAPP_nat_real(v4, % 237.74/37.13 | all_1135_1) = v5 & hBOOL(v3) = v9 & hBOOL(v2) = v8 & $i(v7) & % 237.74/37.13 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = % 237.74/37.13 | v5)))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (410) implies: % 237.74/37.13 | (411) number_number_of_nat(all_1135_2) = all_1135_1 % 237.74/37.13 | (412) bit0(all_1135_3) = all_1135_2 % 237.74/37.13 | (413) bit1(pls) = all_1135_3 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (96) with fresh symbols all_1138_0, all_1138_1, % 237.74/37.13 | all_1138_2, all_1138_3 gives: % 237.74/37.13 | (414) bit1(pls) = all_1138_3 & bit0(all_1138_3) = all_1138_2 & % 237.74/37.13 | number_number_of_nat(all_1138_2) = all_1138_1 & % 237.74/37.13 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1138_0 & % 237.74/37.13 | $i(all_1138_0) & $i(all_1138_1) & $i(all_1138_2) & $i(all_1138_3) & % 237.74/37.13 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 237.74/37.13 | (hAPP_int_bool(all_1138_0, v1) = v3) | ~ % 237.74/37.13 | (hAPP_int_bool(all_1138_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 237.74/37.13 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : % 237.74/37.13 | ? [v9: any] : (power_power_int(v1) = v6 & power_power_int(v0) = v4 % 237.74/37.13 | & hAPP_nat_int(v6, all_1138_1) = v7 & hAPP_nat_int(v4, % 237.74/37.13 | all_1138_1) = v5 & hBOOL(v3) = v9 & hBOOL(v2) = v8 & $i(v7) & % 237.74/37.13 | $i(v6) & $i(v5) & $i(v4) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = % 237.74/37.13 | v5)))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (414) implies: % 237.74/37.13 | (415) number_number_of_nat(all_1138_2) = all_1138_1 % 237.74/37.13 | (416) bit0(all_1138_3) = all_1138_2 % 237.74/37.13 | (417) bit1(pls) = all_1138_3 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (91) with fresh symbols all_1144_0, all_1144_1, % 237.74/37.13 | all_1144_2, all_1144_3 gives: % 237.74/37.13 | (418) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_1144_0 % 237.74/37.13 | & bit1(pls) = all_1144_3 & bit0(all_1144_3) = all_1144_2 & % 237.74/37.13 | number_number_of_nat(all_1144_2) = all_1144_1 & $i(all_1144_0) & % 237.74/37.13 | $i(all_1144_1) & $i(all_1144_2) & $i(all_1144_3) & ! [v0: $i] : ! % 237.74/37.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.74/37.13 | [v6: $i] : ! [v7: $i] : ( ~ % 237.74/37.13 | (hAPP_r1134773055l_bool(ord_less_eq_real, v3) = v4) | ~ % 237.74/37.13 | (power_power_real(v1) = v5) | ~ (power_power_real(v0) = v2) | ~ % 237.74/37.13 | (hAPP_nat_real(v5, all_1144_1) = v6) | ~ (hAPP_nat_real(v2, % 237.74/37.13 | all_1144_1) = v3) | ~ (hAPP_real_bool(v4, v6) = v7) | ~ % 237.74/37.13 | $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 237.74/37.13 | ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 237.74/37.13 | (hAPP_r1134773055l_bool(ord_less_eq_real, v0) = v11 & hBOOL(v12) = % 237.74/37.13 | v13 & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP_real_bool(v11, v1) % 237.74/37.13 | = v12 & hAPP_real_bool(all_1144_0, v1) = v9 & $i(v12) & $i(v11) & % 237.74/37.13 | $i(v9) & ( ~ (v10 = 0) | ~ (v8 = 0) | v13 = 0))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (418) implies: % 237.74/37.13 | (419) number_number_of_nat(all_1144_2) = all_1144_1 % 237.74/37.13 | (420) bit0(all_1144_3) = all_1144_2 % 237.74/37.13 | (421) bit1(pls) = all_1144_3 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (92) with fresh symbols all_1150_0, all_1150_1, % 237.74/37.13 | all_1150_2, all_1150_3 gives: % 237.74/37.13 | (422) hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = all_1150_0 & % 237.74/37.13 | bit1(pls) = all_1150_3 & bit0(all_1150_3) = all_1150_2 & % 237.74/37.13 | number_number_of_nat(all_1150_2) = all_1150_1 & $i(all_1150_0) & % 237.74/37.13 | $i(all_1150_1) & $i(all_1150_2) & $i(all_1150_3) & ! [v0: $i] : ! % 237.74/37.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.74/37.13 | [v6: $i] : ! [v7: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_eq_nat, % 237.74/37.13 | v3) = v4) | ~ (power_power_nat(v1) = v5) | ~ % 237.74/37.13 | (power_power_nat(v0) = v2) | ~ (hAPP_nat_nat(v5, all_1150_1) = v6) % 237.74/37.13 | | ~ (hAPP_nat_nat(v2, all_1150_1) = v3) | ~ (hAPP_nat_bool(v4, % 237.74/37.13 | v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] % 237.74/37.13 | : ? [v10: any] : ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 237.74/37.13 | (hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v11 & hBOOL(v12) = % 237.74/37.13 | v13 & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP_nat_bool(v11, v1) = % 237.74/37.13 | v12 & hAPP_nat_bool(all_1150_0, v1) = v9 & $i(v12) & $i(v11) & % 237.74/37.13 | $i(v9) & ( ~ (v10 = 0) | ~ (v8 = 0) | v13 = 0))) % 237.74/37.13 | % 237.74/37.13 | ALPHA: (422) implies: % 237.74/37.13 | (423) number_number_of_nat(all_1150_2) = all_1150_1 % 237.74/37.13 | (424) bit0(all_1150_3) = all_1150_2 % 237.74/37.13 | (425) bit1(pls) = all_1150_3 % 237.74/37.13 | % 237.74/37.13 | DELTA: instantiating (98) with fresh symbols all_1159_0, all_1159_1, % 237.74/37.13 | all_1159_2, all_1159_3 gives: % 237.74/37.13 | (426) hAPP_n1699378549t_bool(ord_less_eq_nat, zero_zero_nat) = all_1159_0 & % 237.74/37.13 | bit1(pls) = all_1159_3 & bit0(all_1159_3) = all_1159_2 & % 237.74/37.13 | number_number_of_nat(all_1159_2) = all_1159_1 & $i(all_1159_0) & % 237.74/37.13 | $i(all_1159_1) & $i(all_1159_2) & $i(all_1159_3) & ! [v0: $i] : ! % 237.74/37.13 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 237.74/37.13 | [v6: $i] : ! [v7: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_nat, % 237.74/37.13 | v3) = v4) | ~ (power_power_nat(v1) = v5) | ~ % 237.74/37.13 | (power_power_nat(v0) = v2) | ~ (hAPP_nat_nat(v5, all_1159_1) = v6) % 237.74/37.13 | | ~ (hAPP_nat_nat(v2, all_1159_1) = v3) | ~ (hAPP_nat_bool(v4, % 237.74/37.14 | v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] % 237.74/37.14 | : ? [v10: any] : ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 237.74/37.14 | (hAPP_n1699378549t_bool(ord_less_nat, v0) = v11 & hBOOL(v12) = v13 % 237.74/37.14 | & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP_nat_bool(v11, v1) = v12 % 237.74/37.14 | & hAPP_nat_bool(all_1159_0, v1) = v9 & $i(v12) & $i(v11) & $i(v9) % 237.74/37.14 | & ( ~ (v10 = 0) | ~ (v8 = 0) | v13 = 0))) % 237.74/37.14 | % 237.74/37.14 | ALPHA: (426) implies: % 237.74/37.14 | (427) number_number_of_nat(all_1159_2) = all_1159_1 % 237.74/37.14 | (428) bit0(all_1159_3) = all_1159_2 % 237.74/37.14 | (429) bit1(pls) = all_1159_3 % 237.74/37.14 | % 237.74/37.14 | DELTA: instantiating (55) with fresh symbol all_1162_0 gives: % 238.06/37.14 | (430) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1162_0 & % 238.06/37.14 | $i(all_1162_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 238.06/37.14 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 238.06/37.14 | (power_power_int(v0) = v3) | ~ % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_int, v4) = v5) | ~ % 238.06/37.14 | (hAPP_nat_int(v3, v2) = v4) | ~ (hAPP_nat_int(v3, v1) = v6) | ~ % 238.06/37.14 | (hAPP_int_bool(v5, v6) = v7) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 238.06/37.14 | ? [v8: $i] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: % 238.06/37.14 | any] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: % 238.06/37.14 | any] : (hAPP_n1699378549t_bool(ord_less_nat, v1) = v8 & % 238.06/37.14 | hAPP_i1948725293t_bool(ord_less_int, v0) = v13 & hBOOL(v14) = v15 % 238.06/37.14 | & hBOOL(v11) = v12 & hBOOL(v9) = v10 & hBOOL(v7) = v16 & % 238.06/37.14 | hAPP_nat_bool(v8, v2) = v9 & hAPP_int_bool(v13, one_one_int) = % 238.06/37.14 | v14 & hAPP_int_bool(all_1162_0, v0) = v11 & $i(v14) & $i(v13) & % 238.06/37.14 | $i(v11) & $i(v9) & $i(v8) & ( ~ (v15 = 0) | ~ (v12 = 0) | ~ % 238.06/37.14 | (v10 = 0) | v16 = 0))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (430) implies: % 238.06/37.14 | (431) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1162_0 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (93) with fresh symbols all_1165_0, all_1165_1, % 238.06/37.14 | all_1165_2, all_1165_3 gives: % 238.06/37.14 | (432) bit1(pls) = all_1165_3 & bit0(all_1165_3) = all_1165_2 & % 238.06/37.14 | number_number_of_nat(all_1165_2) = all_1165_1 & % 238.06/37.14 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1165_0 & % 238.06/37.14 | $i(all_1165_0) & $i(all_1165_1) & $i(all_1165_2) & $i(all_1165_3) & % 238.06/37.14 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 238.06/37.14 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(v1) = % 238.06/37.14 | v5) | ~ (power_power_int(v0) = v2) | ~ % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4) | ~ % 238.06/37.14 | (hAPP_nat_int(v5, all_1165_1) = v6) | ~ (hAPP_nat_int(v2, % 238.06/37.14 | all_1165_1) = v3) | ~ (hAPP_int_bool(v4, v6) = v7) | ~ $i(v1) % 238.06/37.14 | | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: % 238.06/37.14 | $i] : ? [v12: $i] : ? [v13: any] : % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v11 & hBOOL(v12) = % 238.06/37.14 | v13 & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP_int_bool(v11, v1) = % 238.06/37.14 | v12 & hAPP_int_bool(all_1165_0, v1) = v9 & $i(v12) & $i(v11) & % 238.06/37.14 | $i(v9) & ( ~ (v10 = 0) | ~ (v8 = 0) | v13 = 0))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (432) implies: % 238.06/37.14 | (433) number_number_of_nat(all_1165_2) = all_1165_1 % 238.06/37.14 | (434) bit0(all_1165_3) = all_1165_2 % 238.06/37.14 | (435) bit1(pls) = all_1165_3 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (97) with fresh symbols all_1171_0, all_1171_1, % 238.06/37.14 | all_1171_2, all_1171_3 gives: % 238.06/37.14 | (436) hAPP_r1134773055l_bool(ord_less_eq_real, zero_zero_real) = all_1171_0 % 238.06/37.14 | & bit1(pls) = all_1171_3 & bit0(all_1171_3) = all_1171_2 & % 238.06/37.14 | number_number_of_nat(all_1171_2) = all_1171_1 & $i(all_1171_0) & % 238.06/37.14 | $i(all_1171_1) & $i(all_1171_2) & $i(all_1171_3) & ! [v0: $i] : ! % 238.06/37.14 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 238.06/37.14 | [v6: $i] : ! [v7: $i] : ( ~ (hAPP_r1134773055l_bool(ord_less_real, % 238.06/37.14 | v3) = v4) | ~ (power_power_real(v1) = v5) | ~ % 238.06/37.14 | (power_power_real(v0) = v2) | ~ (hAPP_nat_real(v5, all_1171_1) = % 238.06/37.14 | v6) | ~ (hAPP_nat_real(v2, all_1171_1) = v3) | ~ % 238.06/37.14 | (hAPP_real_bool(v4, v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: % 238.06/37.14 | any] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: $i] % 238.06/37.14 | : ? [v13: any] : (hAPP_r1134773055l_bool(ord_less_real, v0) = v11 % 238.06/37.14 | & hBOOL(v12) = v13 & hBOOL(v9) = v10 & hBOOL(v7) = v8 & % 238.06/37.14 | hAPP_real_bool(v11, v1) = v12 & hAPP_real_bool(all_1171_0, v1) = % 238.06/37.14 | v9 & $i(v12) & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ~ (v8 = 0) | % 238.06/37.14 | v13 = 0))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (436) implies: % 238.06/37.14 | (437) number_number_of_nat(all_1171_2) = all_1171_1 % 238.06/37.14 | (438) bit0(all_1171_3) = all_1171_2 % 238.06/37.14 | (439) bit1(pls) = all_1171_3 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (99) with fresh symbols all_1174_0, all_1174_1, % 238.06/37.14 | all_1174_2, all_1174_3 gives: % 238.06/37.14 | (440) bit1(pls) = all_1174_3 & bit0(all_1174_3) = all_1174_2 & % 238.06/37.14 | number_number_of_nat(all_1174_2) = all_1174_1 & % 238.06/37.14 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1174_0 & % 238.06/37.14 | $i(all_1174_0) & $i(all_1174_1) & $i(all_1174_2) & $i(all_1174_3) & % 238.06/37.14 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 238.06/37.14 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(v1) = % 238.06/37.14 | v5) | ~ (power_power_int(v0) = v2) | ~ % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_int, v3) = v4) | ~ % 238.06/37.14 | (hAPP_nat_int(v5, all_1174_1) = v6) | ~ (hAPP_nat_int(v2, % 238.06/37.14 | all_1174_1) = v3) | ~ (hAPP_int_bool(v4, v6) = v7) | ~ $i(v1) % 238.06/37.14 | | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: % 238.06/37.14 | $i] : ? [v12: $i] : ? [v13: any] : % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v11 & hBOOL(v12) = v13 % 238.06/37.14 | & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP_int_bool(v11, v1) = v12 % 238.06/37.14 | & hAPP_int_bool(all_1174_0, v1) = v9 & $i(v12) & $i(v11) & $i(v9) % 238.06/37.14 | & ( ~ (v10 = 0) | ~ (v8 = 0) | v13 = 0))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (440) implies: % 238.06/37.14 | (441) number_number_of_nat(all_1174_2) = all_1174_1 % 238.06/37.14 | (442) bit0(all_1174_3) = all_1174_2 % 238.06/37.14 | (443) bit1(pls) = all_1174_3 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (69) with fresh symbol all_1183_0 gives: % 238.06/37.14 | (444) plus_plus_nat(one_one_nat) = all_1183_0 & $i(all_1183_0) & ! [v0: % 238.06/37.14 | $i] : ! [v1: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = % 238.06/37.14 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? % 238.06/37.14 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (succ(v0) = v6 & % 238.06/37.14 | hAPP_nat_nat(all_1183_0, v4) = v5 & number_number_of_nat(v6) = v7 % 238.06/37.14 | & number_number_of_nat(v0) = v4 & hBOOL(v2) = v3 & % 238.06/37.14 | hAPP_int_bool(v1, pls) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 238.06/37.14 | $i(v2) & (v7 = v5 | v3 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 238.06/37.14 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.14 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 238.06/37.14 | (hAPP_nat_nat(all_1183_0, v4) = v5 & number_number_of_nat(v0) = v4 % 238.06/37.14 | & hBOOL(v2) = v3 & hAPP_int_bool(v1, pls) = v2 & $i(v5) & $i(v4) % 238.06/37.14 | & $i(v2) & ( ~ (v3 = 0) | v5 = one_one_nat))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (444) implies: % 238.06/37.14 | (445) plus_plus_nat(one_one_nat) = all_1183_0 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (109) with fresh symbols all_1186_0, all_1186_1, % 238.06/37.14 | all_1186_2, all_1186_3 gives: % 238.06/37.14 | (446) number_number_of_int(all_1186_2) = all_1186_0 & bit1(pls) = % 238.06/37.14 | all_1186_3 & bit0(all_1186_3) = all_1186_2 & % 238.06/37.14 | number_number_of_nat(all_1186_2) = all_1186_1 & $i(all_1186_0) & % 238.06/37.14 | $i(all_1186_1) & $i(all_1186_2) & $i(all_1186_3) & ! [v0: $i] : ! % 238.06/37.14 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 238.06/37.14 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 238.06/37.14 | ! [v11: $i] : ( ~ (times_times_int(v5, v1) = v6) | ~ % 238.06/37.14 | (times_times_int(all_1186_0, v0) = v5) | ~ (power_power_int(v1) = % 238.06/37.14 | v9) | ~ (power_power_int(v0) = v2) | ~ (plus_plus_int(v7) = v8) % 238.06/37.14 | | ~ (plus_plus_int(v3) = v4) | ~ (hAPP_nat_int(v9, all_1186_1) = % 238.06/37.14 | v10) | ~ (hAPP_nat_int(v2, all_1186_1) = v3) | ~ % 238.06/37.14 | (hAPP_int_int(v8, v10) = v11) | ~ (hAPP_int_int(v4, v6) = v7) | ~ % 238.06/37.14 | $i(v1) | ~ $i(v0) | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 238.06/37.14 | (power_power_int(v13) = v14 & plus_plus_int(v0) = v12 & % 238.06/37.14 | hAPP_nat_int(v14, all_1186_1) = v11 & hAPP_int_int(v12, v1) = v13 % 238.06/37.14 | & $i(v14) & $i(v13) & $i(v12) & $i(v11))) % 238.06/37.14 | % 238.06/37.14 | ALPHA: (446) implies: % 238.06/37.14 | (447) number_number_of_nat(all_1186_2) = all_1186_1 % 238.06/37.14 | (448) bit0(all_1186_3) = all_1186_2 % 238.06/37.14 | (449) bit1(pls) = all_1186_3 % 238.06/37.14 | % 238.06/37.14 | DELTA: instantiating (41) with fresh symbols all_1204_0, all_1204_1, % 238.06/37.14 | all_1204_2, all_1204_3 gives: % 238.06/37.15 | (450) bit1(pls) = all_1204_2 & bit0(all_1204_2) = all_1204_1 & % 238.06/37.15 | number_number_of_nat(all_1204_1) = all_1204_0 & % 238.06/37.15 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1204_3 & % 238.06/37.15 | $i(all_1204_0) & $i(all_1204_1) & $i(all_1204_2) & $i(all_1204_3) & % 238.06/37.15 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 238.06/37.15 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (power_power_int(v1) = % 238.06/37.15 | v5) | ~ (power_power_int(v0) = v2) | ~ (plus_plus_int(v3) = v4) % 238.06/37.15 | | ~ (hAPP_nat_int(v5, all_1204_0) = v6) | ~ (hAPP_nat_int(v2, % 238.06/37.15 | all_1204_0) = v3) | ~ (hAPP_int_int(v4, v6) = v7) | ~ $i(v1) % 238.06/37.15 | | ~ $i(v0) | ? [v8: $i] : (hBOOL(v8) = 0 & % 238.06/37.15 | hAPP_int_bool(all_1204_3, v7) = v8 & $i(v8)) | (v1 = % 238.06/37.15 | zero_zero_int & v0 = zero_zero_int)) & ! [v0: $i] : ! [v1: $i] % 238.06/37.15 | : ! [v2: $i] : ! [v3: $i] : ( ~ (power_power_int(zero_zero_int) = % 238.06/37.15 | v0) | ~ (plus_plus_int(v1) = v2) | ~ (hAPP_nat_int(v0, % 238.06/37.15 | all_1204_0) = v1) | ~ (hAPP_int_int(v2, v1) = v3) | ? [v4: % 238.06/37.15 | $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & % 238.06/37.15 | hAPP_int_bool(all_1204_3, v3) = v4 & $i(v4))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (450) implies: % 238.06/37.15 | (451) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1204_3 % 238.06/37.15 | (452) number_number_of_nat(all_1204_1) = all_1204_0 % 238.06/37.15 | (453) bit0(all_1204_2) = all_1204_1 % 238.06/37.15 | (454) bit1(pls) = all_1204_2 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (42) with fresh symbols all_1207_0, all_1207_1, % 238.06/37.15 | all_1207_2, all_1207_3 gives: % 238.06/37.15 | (455) hAPP_r1134773055l_bool(ord_less_real, zero_zero_real) = all_1207_3 & % 238.06/37.15 | bit1(pls) = all_1207_2 & bit0(all_1207_2) = all_1207_1 & % 238.06/37.15 | number_number_of_nat(all_1207_1) = all_1207_0 & $i(all_1207_0) & % 238.06/37.15 | $i(all_1207_1) & $i(all_1207_2) & $i(all_1207_3) & ! [v0: $i] : ! % 238.06/37.15 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 238.06/37.15 | [v6: $i] : ! [v7: $i] : ( ~ (plus_plus_real(v3) = v4) | ~ % 238.06/37.15 | (power_power_real(v1) = v5) | ~ (power_power_real(v0) = v2) | ~ % 238.06/37.15 | (hAPP_nat_real(v5, all_1207_0) = v6) | ~ (hAPP_nat_real(v2, % 238.06/37.15 | all_1207_0) = v3) | ~ (hAPP_real_real(v4, v6) = v7) | ~ % 238.06/37.15 | $i(v1) | ~ $i(v0) | ? [v8: $i] : (hBOOL(v8) = 0 & % 238.06/37.15 | hAPP_real_bool(all_1207_3, v7) = v8 & $i(v8)) | (v1 = % 238.06/37.15 | zero_zero_real & v0 = zero_zero_real)) & ! [v0: $i] : ! [v1: % 238.06/37.15 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus_real(v1) = v2) | % 238.06/37.15 | ~ (power_power_real(zero_zero_real) = v0) | ~ (hAPP_nat_real(v0, % 238.06/37.15 | all_1207_0) = v1) | ~ (hAPP_real_real(v2, v1) = v3) | ? [v4: % 238.06/37.15 | $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & % 238.06/37.15 | hAPP_real_bool(all_1207_3, v3) = v4 & $i(v4))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (455) implies: % 238.06/37.15 | (456) number_number_of_nat(all_1207_1) = all_1207_0 % 238.06/37.15 | (457) bit0(all_1207_2) = all_1207_1 % 238.06/37.15 | (458) bit1(pls) = all_1207_2 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (73) with fresh symbol all_1210_0 gives: % 238.06/37.15 | (459) bit1(pls) = all_1210_0 & $i(all_1210_0) & ! [v0: $i] : ! [v1: $i] : % 238.06/37.15 | ( ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v1) | ~ $i(v0) | % 238.06/37.15 | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 238.06/37.15 | : ? [v7: any] : (hAPP_r1134773055l_bool(ord_less_eq_real, v4) = v5 % 238.06/37.15 | & number267125858f_real(v0) = v4 & hBOOL(v6) = v7 & hBOOL(v2) = % 238.06/37.15 | v3 & hAPP_real_bool(v5, one_one_real) = v6 & hAPP_int_bool(v1, % 238.06/37.15 | all_1210_0) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & ( ~ (v3 % 238.06/37.15 | = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 238.06/37.15 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.15 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 238.06/37.15 | ? [v7: any] : (hAPP_r1134773055l_bool(ord_less_eq_real, v2) = v3 & % 238.06/37.15 | number267125858f_real(v0) = v2 & hBOOL(v6) = v7 & hBOOL(v4) = v5 % 238.06/37.15 | & hAPP_real_bool(v3, one_one_real) = v4 & hAPP_int_bool(v1, % 238.06/37.15 | all_1210_0) = v6 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v5 % 238.06/37.15 | = 0) | v7 = 0))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (459) implies: % 238.06/37.15 | (460) bit1(pls) = all_1210_0 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (24) with fresh symbol all_1213_0 gives: % 238.06/37.15 | (461) bit1(pls) = all_1213_0 & $i(all_1213_0) & ! [v0: $i] : ! [v1: $i] : % 238.06/37.15 | ( ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.15 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 238.06/37.15 | ? [v7: any] : (number_number_of_int(v0) = v4 & % 238.06/37.15 | hAPP_i1948725293t_bool(ord_less_int, v4) = v5 & hBOOL(v6) = v7 & % 238.06/37.15 | hBOOL(v2) = v3 & hAPP_int_bool(v5, one_one_int) = v6 & % 238.06/37.15 | hAPP_int_bool(v1, all_1213_0) = v2 & $i(v6) & $i(v5) & $i(v4) & % 238.06/37.15 | $i(v2) & ( ~ (v3 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 238.06/37.15 | ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.15 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 238.06/37.15 | ? [v7: any] : (number_number_of_int(v0) = v2 & % 238.06/37.15 | hAPP_i1948725293t_bool(ord_less_int, v2) = v3 & hBOOL(v6) = v7 & % 238.06/37.15 | hBOOL(v4) = v5 & hAPP_int_bool(v3, one_one_int) = v4 & % 238.06/37.15 | hAPP_int_bool(v1, all_1213_0) = v6 & $i(v6) & $i(v4) & $i(v3) & % 238.06/37.15 | $i(v2) & ( ~ (v5 = 0) | v7 = 0))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (461) implies: % 238.06/37.15 | (462) bit1(pls) = all_1213_0 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (25) with fresh symbol all_1216_0 gives: % 238.06/37.15 | (463) bit1(pls) = all_1216_0 & $i(all_1216_0) & ! [v0: $i] : ! [v1: $i] : % 238.06/37.15 | ( ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.15 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 238.06/37.15 | ? [v7: any] : (hAPP_r1134773055l_bool(ord_less_real, v4) = v5 & % 238.06/37.15 | number267125858f_real(v0) = v4 & hBOOL(v6) = v7 & hBOOL(v2) = v3 % 238.06/37.15 | & hAPP_real_bool(v5, one_one_real) = v6 & hAPP_int_bool(v1, % 238.06/37.15 | all_1216_0) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & ( ~ (v3 % 238.06/37.15 | = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 238.06/37.15 | (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? % 238.06/37.15 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 238.06/37.15 | ? [v7: any] : (hAPP_r1134773055l_bool(ord_less_real, v2) = v3 & % 238.06/37.15 | number267125858f_real(v0) = v2 & hBOOL(v6) = v7 & hBOOL(v4) = v5 % 238.06/37.15 | & hAPP_real_bool(v3, one_one_real) = v4 & hAPP_int_bool(v1, % 238.06/37.15 | all_1216_0) = v6 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v5 % 238.06/37.15 | = 0) | v7 = 0))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (463) implies: % 238.06/37.15 | (464) bit1(pls) = all_1216_0 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (74) with fresh symbol all_1221_0 gives: % 238.06/37.15 | (465) bit1(pls) = all_1221_0 & $i(all_1221_0) & ! [v0: $i] : ! [v1: $i] : % 238.06/37.15 | ( ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v1) | ~ $i(v0) | % 238.06/37.15 | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 238.06/37.15 | : ? [v7: any] : (number_number_of_int(v0) = v4 & % 238.06/37.15 | hAPP_i1948725293t_bool(ord_less_eq_int, v4) = v5 & hBOOL(v6) = v7 % 238.06/37.15 | & hBOOL(v2) = v3 & hAPP_int_bool(v5, one_one_int) = v6 & % 238.06/37.15 | hAPP_int_bool(v1, all_1221_0) = v2 & $i(v6) & $i(v5) & $i(v4) & % 238.06/37.15 | $i(v2) & ( ~ (v3 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 238.06/37.15 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v1) | ~ $i(v0) | % 238.06/37.15 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] % 238.06/37.15 | : ? [v7: any] : (number_number_of_int(v0) = v2 & % 238.06/37.15 | hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v3 & hBOOL(v6) = v7 % 238.06/37.15 | & hBOOL(v4) = v5 & hAPP_int_bool(v3, one_one_int) = v4 & % 238.06/37.15 | hAPP_int_bool(v1, all_1221_0) = v6 & $i(v6) & $i(v4) & $i(v3) & % 238.06/37.15 | $i(v2) & ( ~ (v5 = 0) | v7 = 0))) % 238.06/37.15 | % 238.06/37.15 | ALPHA: (465) implies: % 238.06/37.15 | (466) bit1(pls) = all_1221_0 % 238.06/37.15 | % 238.06/37.15 | DELTA: instantiating (102) with fresh symbols all_1224_0, all_1224_1, % 238.06/37.15 | all_1224_2 gives: % 238.06/37.16 | (467) bit1(pls) = all_1224_2 & bit0(all_1224_2) = all_1224_1 & % 238.06/37.16 | number_number_of_nat(all_1224_1) = all_1224_0 & $i(all_1224_0) & % 238.06/37.16 | $i(all_1224_1) & $i(all_1224_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 238.06/37.16 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 238.06/37.16 | [v7: $i] : ( ~ (plus_plus_real(v3) = v4) | ~ (power_power_real(v1) = % 238.06/37.16 | v5) | ~ (power_power_real(v0) = v2) | ~ (hAPP_nat_real(v5, % 238.06/37.16 | all_1224_0) = v6) | ~ (hAPP_nat_real(v2, all_1224_0) = v3) | % 238.06/37.16 | ~ (hAPP_real_real(v4, v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: % 238.06/37.16 | $i] : ? [v9: $i] : ? [v10: int] : ( ~ (v10 = 0) & % 238.06/37.16 | hAPP_r1134773055l_bool(ord_less_eq_real, v7) = v8 & hBOOL(v9) = % 238.06/37.16 | v10 & hAPP_real_bool(v8, zero_zero_real) = v9 & $i(v9) & $i(v8)) % 238.06/37.16 | | (v1 = zero_zero_real & v0 = zero_zero_real)) & ! [v0: $i] : ! % 238.06/37.16 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus_real(v1) = v2) % 238.06/37.16 | | ~ (power_power_real(zero_zero_real) = v0) | ~ % 238.06/37.16 | (hAPP_nat_real(v0, all_1224_0) = v1) | ~ (hAPP_real_real(v2, v1) = % 238.06/37.16 | v3) | ? [v4: $i] : ? [v5: $i] : % 238.06/37.16 | (hAPP_r1134773055l_bool(ord_less_eq_real, v3) = v4 & hBOOL(v5) = 0 % 238.06/37.16 | & hAPP_real_bool(v4, zero_zero_real) = v5 & $i(v5) & $i(v4))) % 238.06/37.16 | % 238.06/37.16 | ALPHA: (467) implies: % 238.06/37.16 | (468) number_number_of_nat(all_1224_1) = all_1224_0 % 238.06/37.16 | (469) bit0(all_1224_2) = all_1224_1 % 238.06/37.16 | (470) bit1(pls) = all_1224_2 % 238.06/37.16 | % 238.06/37.16 | DELTA: instantiating (103) with fresh symbols all_1227_0, all_1227_1, % 238.06/37.16 | all_1227_2 gives: % 238.06/37.16 | (471) bit1(pls) = all_1227_2 & bit0(all_1227_2) = all_1227_1 & % 238.06/37.16 | number_number_of_nat(all_1227_1) = all_1227_0 & $i(all_1227_0) & % 238.06/37.16 | $i(all_1227_1) & $i(all_1227_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 238.06/37.16 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 238.06/37.16 | [v7: $i] : ( ~ (power_power_int(v1) = v5) | ~ (power_power_int(v0) = % 238.06/37.16 | v2) | ~ (plus_plus_int(v3) = v4) | ~ (hAPP_nat_int(v5, % 238.06/37.16 | all_1227_0) = v6) | ~ (hAPP_nat_int(v2, all_1227_0) = v3) | ~ % 238.06/37.16 | (hAPP_int_int(v4, v6) = v7) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : % 238.06/37.16 | ? [v9: $i] : ? [v10: int] : ( ~ (v10 = 0) & % 238.06/37.16 | hAPP_i1948725293t_bool(ord_less_eq_int, v7) = v8 & hBOOL(v9) = % 238.06/37.16 | v10 & hAPP_int_bool(v8, zero_zero_int) = v9 & $i(v9) & $i(v8)) | % 238.06/37.16 | (v1 = zero_zero_int & v0 = zero_zero_int)) & ! [v0: $i] : ! [v1: % 238.06/37.16 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 238.06/37.16 | (power_power_int(zero_zero_int) = v0) | ~ (plus_plus_int(v1) = v2) % 238.06/37.16 | | ~ (hAPP_nat_int(v0, all_1227_0) = v1) | ~ (hAPP_int_int(v2, v1) % 238.06/37.16 | = v3) | ? [v4: $i] : ? [v5: $i] : % 238.06/37.16 | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4 & hBOOL(v5) = 0 & % 238.06/37.16 | hAPP_int_bool(v4, zero_zero_int) = v5 & $i(v5) & $i(v4))) % 238.06/37.16 | % 238.06/37.16 | ALPHA: (471) implies: % 238.06/37.16 | (472) number_number_of_nat(all_1227_1) = all_1227_0 % 238.06/37.16 | (473) bit0(all_1227_2) = all_1227_1 % 238.06/37.16 | (474) bit1(pls) = all_1227_2 % 238.06/37.16 | % 238.06/37.16 | DELTA: instantiating (28) with fresh symbol all_1238_0 gives: % 238.06/37.16 | (475) plus_plus_int(one_one_int) = all_1238_0 & $i(all_1238_0) & ! [v0: % 238.06/37.16 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 238.06/37.16 | (plus_plus_int(v1) = v2) | ~ (hAPP_int_int(v2, v0) = v3) | ~ % 238.06/37.16 | (hAPP_int_int(all_1238_0, v0) = v1) | ~ $i(v0) | ? [v4: $i] : ? % 238.06/37.16 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] % 238.06/37.16 | : (hAPP_i1948725293t_bool(ord_less_int, v3) = v7 & % 238.06/37.16 | hAPP_i1948725293t_bool(ord_less_int, v0) = v4 & hBOOL(v8) = v9 & % 238.06/37.16 | hBOOL(v5) = v6 & hAPP_int_bool(v7, zero_zero_int) = v8 & % 238.06/37.16 | hAPP_int_bool(v4, zero_zero_int) = v5 & $i(v8) & $i(v7) & $i(v5) % 238.06/37.16 | & $i(v4) & ( ~ (v6 = 0) | v9 = 0))) & ! [v0: $i] : ! [v1: $i] : % 238.06/37.16 | ! [v2: $i] : ! [v3: $i] : ( ~ (plus_plus_int(v1) = v2) | ~ % 238.06/37.16 | (hAPP_int_int(v2, v0) = v3) | ~ (hAPP_int_int(all_1238_0, v0) = % 238.06/37.16 | v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? % 238.06/37.16 | [v7: $i] : ? [v8: $i] : ? [v9: any] : % 238.06/37.16 | (hAPP_i1948725293t_bool(ord_less_int, v3) = v4 & % 238.06/37.16 | hAPP_i1948725293t_bool(ord_less_int, v0) = v7 & hBOOL(v8) = v9 & % 238.06/37.16 | hBOOL(v5) = v6 & hAPP_int_bool(v7, zero_zero_int) = v8 & % 238.06/37.16 | hAPP_int_bool(v4, zero_zero_int) = v5 & $i(v8) & $i(v7) & $i(v5) % 238.06/37.16 | & $i(v4) & ( ~ (v6 = 0) | v9 = 0))) % 238.06/37.16 | % 238.06/37.16 | ALPHA: (475) implies: % 238.06/37.16 | (476) plus_plus_int(one_one_int) = all_1238_0 % 238.06/37.16 | % 238.06/37.16 | DELTA: instantiating (58) with fresh symbol all_1241_0 gives: % 238.06/37.16 | (477) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1241_0 & % 238.06/37.16 | $i(all_1241_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 238.06/37.16 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 238.06/37.16 | (hAPP_n1699378549t_bool(ord_less_nat, v2) = v3) | ~ % 238.06/37.16 | (number_number_of_nat(v1) = v4) | ~ (number_number_of_nat(v0) = % 238.06/37.16 | v2) | ~ (hAPP_nat_bool(v3, v4) = v5) | ~ $i(v1) | ~ $i(v0) | % 238.06/37.16 | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: % 238.06/37.16 | $i] : ? [v11: any] : (hAPP_i1948725293t_bool(ord_less_int, v0) = % 238.06/37.16 | v7 & hBOOL(v10) = v11 & hBOOL(v8) = v9 & hBOOL(v5) = v6 & % 238.06/37.16 | hAPP_int_bool(v7, v1) = v8 & hAPP_int_bool(all_1241_0, v1) = v10 % 238.06/37.16 | & $i(v10) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v11 = 0 & v9 = % 238.06/37.16 | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 238.06/37.16 | : ! [v4: $i] : ! [v5: $i] : ( ~ % 238.06/37.16 | (hAPP_n1699378549t_bool(ord_less_nat, v2) = v3) | ~ % 238.06/37.16 | (number_number_of_nat(v1) = v4) | ~ (number_number_of_nat(v0) = % 238.06/37.16 | v2) | ~ (hAPP_nat_bool(v3, v4) = v5) | ~ $i(v1) | ~ $i(v0) | % 238.06/37.16 | ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: % 238.06/37.16 | any] : ? [v11: any] : (hAPP_i1948725293t_bool(ord_less_int, v0) % 238.06/37.16 | = v6 & hBOOL(v9) = v10 & hBOOL(v7) = v8 & hBOOL(v5) = v11 & % 238.06/37.16 | hAPP_int_bool(v6, v1) = v7 & hAPP_int_bool(all_1241_0, v1) = v9 & % 238.06/37.16 | $i(v9) & $i(v7) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | v11 = % 238.06/37.16 | 0))) % 238.06/37.16 | % 238.06/37.16 | ALPHA: (477) implies: % 238.06/37.16 | (478) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1241_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (161) imply: % 238.06/37.16 | (479) number_number_of_int(zero_zero_int) = all_594_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (159) imply: % 238.06/37.16 | (480) number_number_of_int(zero_zero_int) = all_580_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (149) imply: % 238.06/37.16 | (481) number_number_of_int(zero_zero_int) = all_500_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (30) imply: % 238.06/37.16 | (482) number_number_of_int(zero_zero_int) = zero_zero_int % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (474) imply: % 238.06/37.16 | (483) bit1(zero_zero_int) = all_1227_2 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (470) imply: % 238.06/37.16 | (484) bit1(zero_zero_int) = all_1224_2 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (466) imply: % 238.06/37.16 | (485) bit1(zero_zero_int) = all_1221_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (464) imply: % 238.06/37.16 | (486) bit1(zero_zero_int) = all_1216_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (462) imply: % 238.06/37.16 | (487) bit1(zero_zero_int) = all_1213_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (460) imply: % 238.06/37.16 | (488) bit1(zero_zero_int) = all_1210_0 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (458) imply: % 238.06/37.16 | (489) bit1(zero_zero_int) = all_1207_2 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (454) imply: % 238.06/37.16 | (490) bit1(zero_zero_int) = all_1204_2 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (449) imply: % 238.06/37.16 | (491) bit1(zero_zero_int) = all_1186_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (443) imply: % 238.06/37.16 | (492) bit1(zero_zero_int) = all_1174_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (439) imply: % 238.06/37.16 | (493) bit1(zero_zero_int) = all_1171_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (435) imply: % 238.06/37.16 | (494) bit1(zero_zero_int) = all_1165_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (429) imply: % 238.06/37.16 | (495) bit1(zero_zero_int) = all_1159_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (425) imply: % 238.06/37.16 | (496) bit1(zero_zero_int) = all_1150_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (421) imply: % 238.06/37.16 | (497) bit1(zero_zero_int) = all_1144_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (417) imply: % 238.06/37.16 | (498) bit1(zero_zero_int) = all_1138_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (413) imply: % 238.06/37.16 | (499) bit1(zero_zero_int) = all_1135_3 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (409) imply: % 238.06/37.16 | (500) bit1(zero_zero_int) = all_1132_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (407) imply: % 238.06/37.16 | (501) bit1(zero_zero_int) = all_1123_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (405) imply: % 238.06/37.16 | (502) bit1(zero_zero_int) = all_1111_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (403) imply: % 238.06/37.16 | (503) bit1(zero_zero_int) = all_1105_1 % 238.06/37.16 | % 238.06/37.16 | REDUCE: (29), (401) imply: % 238.06/37.17 | (504) bit1(zero_zero_int) = all_1102_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (382) imply: % 238.06/37.17 | (505) bit1(zero_zero_int) = all_1036_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (377) imply: % 238.06/37.17 | (506) bit1(zero_zero_int) = all_1018_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (371) imply: % 238.06/37.17 | (507) bit1(zero_zero_int) = all_952_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (364) imply: % 238.06/37.17 | (508) bit1(zero_zero_int) = all_943_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (360) imply: % 238.06/37.17 | (509) bit1(zero_zero_int) = all_940_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (356) imply: % 238.06/37.17 | (510) bit1(zero_zero_int) = all_937_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (350) imply: % 238.06/37.17 | (511) bit1(zero_zero_int) = all_928_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (342) imply: % 238.06/37.17 | (512) bit1(zero_zero_int) = all_895_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (338) imply: % 238.06/37.17 | (513) bit1(zero_zero_int) = all_889_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (333) imply: % 238.06/37.17 | (514) bit1(zero_zero_int) = all_868_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (326) imply: % 238.06/37.17 | (515) bit1(zero_zero_int) = all_844_4 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (322) imply: % 238.06/37.17 | (516) bit1(zero_zero_int) = all_841_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (312) imply: % 238.06/37.17 | (517) bit1(zero_zero_int) = all_784_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (305) imply: % 238.06/37.17 | (518) bit1(zero_zero_int) = all_775_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (301) imply: % 238.06/37.17 | (519) bit1(zero_zero_int) = all_772_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (297) imply: % 238.06/37.17 | (520) bit1(zero_zero_int) = all_769_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (294) imply: % 238.06/37.17 | (521) bit1(zero_zero_int) = all_767_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (285) imply: % 238.06/37.17 | (522) bit1(zero_zero_int) = all_764_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (281) imply: % 238.06/37.17 | (523) bit1(zero_zero_int) = all_755_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (278) imply: % 238.06/37.17 | (524) bit1(zero_zero_int) = all_752_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (275) imply: % 238.06/37.17 | (525) bit1(zero_zero_int) = all_749_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (269) imply: % 238.06/37.17 | (526) bit1(zero_zero_int) = all_728_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (265) imply: % 238.06/37.17 | (527) bit1(zero_zero_int) = all_716_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (263) imply: % 238.06/37.17 | (528) bit1(zero_zero_int) = all_713_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (261) imply: % 238.06/37.17 | (529) bit1(zero_zero_int) = all_710_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (256) imply: % 238.06/37.17 | (530) bit1(zero_zero_int) = all_704_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (254) imply: % 238.06/37.17 | (531) bit1(zero_zero_int) = all_698_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (248) imply: % 238.06/37.17 | (532) bit1(zero_zero_int) = all_687_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (236) imply: % 238.06/37.17 | (533) bit1(zero_zero_int) = all_683_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (229) imply: % 238.06/37.17 | (534) bit1(zero_zero_int) = all_676_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (227) imply: % 238.06/37.17 | (535) bit1(zero_zero_int) = all_674_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (223) imply: % 238.06/37.17 | (536) bit1(zero_zero_int) = all_672_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (219) imply: % 238.06/37.17 | (537) bit1(zero_zero_int) = all_670_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (215) imply: % 238.06/37.17 | (538) bit1(zero_zero_int) = all_668_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (211) imply: % 238.06/37.17 | (539) bit1(zero_zero_int) = all_658_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (207) imply: % 238.06/37.17 | (540) bit1(zero_zero_int) = all_656_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (204) imply: % 238.06/37.17 | (541) bit1(zero_zero_int) = all_651_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (200) imply: % 238.06/37.17 | (542) bit1(zero_zero_int) = all_649_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (196) imply: % 238.06/37.17 | (543) bit1(zero_zero_int) = all_644_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (190) imply: % 238.06/37.17 | (544) bit1(zero_zero_int) = all_639_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (184) imply: % 238.06/37.17 | (545) bit1(zero_zero_int) = all_634_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (179) imply: % 238.06/37.17 | (546) bit1(zero_zero_int) = all_632_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (174) imply: % 238.06/37.17 | (547) bit1(zero_zero_int) = all_630_3 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (172) imply: % 238.06/37.17 | (548) bit1(zero_zero_int) = all_628_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (144) imply: % 238.06/37.17 | (549) bit1(zero_zero_int) = all_459_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (142) imply: % 238.06/37.17 | (550) bit1(zero_zero_int) = all_457_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (140) imply: % 238.06/37.17 | (551) bit1(zero_zero_int) = all_455_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (138) imply: % 238.06/37.17 | (552) bit1(zero_zero_int) = all_453_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (136) imply: % 238.06/37.17 | (553) bit1(zero_zero_int) = all_451_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (134) imply: % 238.06/37.17 | (554) bit1(zero_zero_int) = all_449_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (132) imply: % 238.06/37.17 | (555) bit1(zero_zero_int) = all_447_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (130) imply: % 238.06/37.17 | (556) bit1(zero_zero_int) = all_445_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (128) imply: % 238.06/37.17 | (557) bit1(zero_zero_int) = all_443_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (126) imply: % 238.06/37.17 | (558) bit1(zero_zero_int) = all_441_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (124) imply: % 238.06/37.17 | (559) bit1(zero_zero_int) = all_439_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (478) imply: % 238.06/37.17 | (560) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1241_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (395) imply: % 238.06/37.17 | (561) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1081_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (393) imply: % 238.06/37.17 | (562) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1078_1 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (391) imply: % 238.06/37.17 | (563) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1072_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (386) imply: % 238.06/37.17 | (564) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1054_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (373) imply: % 238.06/37.17 | (565) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_961_0 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (155) imply: % 238.06/37.17 | (566) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_552_2 % 238.06/37.17 | % 238.06/37.17 | REDUCE: (29), (153) imply: % 238.06/37.17 | (567) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_548_2 % 238.06/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (120) with all_685_2, all_767_5, n, % 238.22/37.17 | semiri1621563631at_int, simplifying with (242), (288) gives: % 238.22/37.17 | (568) all_767_5 = all_685_2 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (120) with all_681_2, all_767_5, n, % 238.22/37.17 | semiri1621563631at_int, simplifying with (232), (288) gives: % 238.22/37.17 | (569) all_767_5 = all_681_2 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_612_0, all_641_0, one_one_int, % 238.22/37.17 | simplifying with (163), (192) gives: % 238.22/37.17 | (570) all_641_0 = all_612_0 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_563_0, all_651_3, one_one_int, % 238.22/37.17 | simplifying with (157), (202) gives: % 238.22/37.17 | (571) all_651_3 = all_563_0 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_651_3, all_681_3, one_one_int, % 238.22/37.17 | simplifying with (202), (233) gives: % 238.22/37.17 | (572) all_681_3 = all_651_3 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_641_0, all_681_3, one_one_int, % 238.22/37.17 | simplifying with (192), (233) gives: % 238.22/37.17 | (573) all_681_3 = all_641_0 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_623_2, all_681_3, one_one_int, % 238.22/37.17 | simplifying with (168), (233) gives: % 238.22/37.17 | (574) all_681_3 = all_623_2 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_681_3, all_685_3, one_one_int, % 238.22/37.17 | simplifying with (233), (243) gives: % 238.22/37.17 | (575) all_685_3 = all_681_3 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_685_3, all_692_0, one_one_int, % 238.22/37.17 | simplifying with (243), (250) gives: % 238.22/37.17 | (576) all_692_0 = all_685_3 % 238.22/37.17 | % 238.22/37.17 | GROUND_INST: instantiating (113) with all_692_0, all_710_2, one_one_int, % 238.22/37.17 | simplifying with (250), (260) gives: % 238.22/37.17 | (577) all_710_2 = all_692_0 % 238.22/37.17 | % 238.22/37.18 | GROUND_INST: instantiating (113) with all_710_2, all_767_6, one_one_int, % 238.22/37.18 | simplifying with (260), (290) gives: % 238.22/37.18 | (578) all_767_6 = all_710_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (113) with all_767_6, all_778_0, one_one_int, % 238.22/37.18 | simplifying with (290), (307) gives: % 238.22/37.18 | (579) all_778_0 = all_767_6 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (113) with all_778_0, all_805_0, one_one_int, % 238.22/37.18 | simplifying with (307), (316) gives: % 238.22/37.18 | (580) all_805_0 = all_778_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (113) with all_805_0, all_1238_0, one_one_int, % 238.22/37.18 | simplifying with (316), (476) gives: % 238.22/37.18 | (581) all_1238_0 = all_805_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (113) with all_658_3, all_1238_0, one_one_int, % 238.22/37.18 | simplifying with (209), (476) gives: % 238.22/37.18 | (582) all_1238_0 = all_658_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_548_2, all_552_2, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (566), (567) gives: % 238.22/37.18 | (583) all_552_2 = all_548_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_552_2, all_623_3, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (169), (566) gives: % 238.22/37.18 | (584) all_623_3 = all_552_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_623_3, all_685_4, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (169), (244) gives: % 238.22/37.18 | (585) all_685_4 = all_623_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_685_4, all_707_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (244), (258) gives: % 238.22/37.18 | (586) all_707_1 = all_685_4 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_548_2, all_734_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (271), (567) gives: % 238.22/37.18 | (587) all_734_0 = all_548_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_707_1, all_778_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (258), (308) gives: % 238.22/37.18 | (588) all_778_1 = all_707_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_778_1, all_835_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (308), (318) gives: % 238.22/37.18 | (589) all_835_0 = all_778_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_835_0, all_856_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (318), (328) gives: % 238.22/37.18 | (590) all_856_0 = all_835_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_856_0, all_901_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (328), (344) gives: % 238.22/37.18 | (591) all_901_0 = all_856_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_901_0, all_907_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (344), (346) gives: % 238.22/37.18 | (592) all_907_0 = all_901_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_907_0, all_931_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (346), (352) gives: % 238.22/37.18 | (593) all_931_1 = all_907_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_931_1, all_946_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (352), (366) gives: % 238.22/37.18 | (594) all_946_0 = all_931_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_946_0, all_961_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (366), (565) gives: % 238.22/37.18 | (595) all_961_0 = all_946_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_961_0, all_1036_3, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (379), (565) gives: % 238.22/37.18 | (596) all_1036_3 = all_961_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1036_3, all_1051_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (379), (384) gives: % 238.22/37.18 | (597) all_1051_1 = all_1036_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1051_1, all_1054_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (384), (564) gives: % 238.22/37.18 | (598) all_1054_0 = all_1051_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1054_0, all_1066_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (388), (564) gives: % 238.22/37.18 | (599) all_1066_1 = all_1054_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1066_1, all_1072_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (388), (563) gives: % 238.22/37.18 | (600) all_1072_0 = all_1066_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1072_0, all_1078_1, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (562), (563) gives: % 238.22/37.18 | (601) all_1078_1 = all_1072_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1078_1, all_1081_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (561), (562) gives: % 238.22/37.18 | (602) all_1081_0 = all_1078_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1081_0, all_1099_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (397), (561) gives: % 238.22/37.18 | (603) all_1099_0 = all_1081_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1099_0, all_1162_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (397), (431) gives: % 238.22/37.18 | (604) all_1162_0 = all_1099_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1072_1, all_1204_3, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (390), (451) gives: % 238.22/37.18 | (605) all_1204_3 = all_1072_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_734_0, all_1204_3, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (271), (451) gives: % 238.22/37.18 | (606) all_1204_3 = all_734_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_519_1, all_1204_3, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (151), (451) gives: % 238.22/37.18 | (607) all_1204_3 = all_519_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_1162_0, all_1241_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (431), (560) gives: % 238.22/37.18 | (608) all_1241_0 = all_1162_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (121) with all_477_1, all_1241_0, zero_zero_int, % 238.22/37.18 | ord_less_int, simplifying with (146), (560) gives: % 238.22/37.18 | (609) all_1241_0 = all_477_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_443_0, all_447_0, zero_zero_int, % 238.22/37.18 | simplifying with (555), (557) gives: % 238.22/37.18 | (610) all_447_0 = all_443_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_453_0, all_455_0, zero_zero_int, % 238.22/37.18 | simplifying with (551), (552) gives: % 238.22/37.18 | (611) all_455_0 = all_453_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_455_0, all_457_0, zero_zero_int, % 238.22/37.18 | simplifying with (550), (551) gives: % 238.22/37.18 | (612) all_457_0 = all_455_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_457_0, all_459_0, zero_zero_int, % 238.22/37.18 | simplifying with (549), (550) gives: % 238.22/37.18 | (613) all_459_0 = all_457_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_459_0, all_628_1, zero_zero_int, % 238.22/37.18 | simplifying with (548), (549) gives: % 238.22/37.18 | (614) all_628_1 = all_459_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_453_0, all_658_1, zero_zero_int, % 238.22/37.18 | simplifying with (539), (552) gives: % 238.22/37.18 | (615) all_658_1 = all_453_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_451_0, all_658_1, zero_zero_int, % 238.22/37.18 | simplifying with (539), (553) gives: % 238.22/37.18 | (616) all_658_1 = all_451_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_639_2, all_683_3, zero_zero_int, % 238.22/37.18 | simplifying with (533), (544) gives: % 238.22/37.18 | (617) all_683_3 = all_639_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_632_1, all_683_3, zero_zero_int, % 238.22/37.18 | simplifying with (533), (546) gives: % 238.22/37.18 | (618) all_683_3 = all_632_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_683_3, all_687_3, zero_zero_int, % 238.22/37.18 | simplifying with (532), (533) gives: % 238.22/37.18 | (619) all_687_3 = all_683_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_676_3, all_704_0, zero_zero_int, % 238.22/37.18 | simplifying with (530), (534) gives: % 238.22/37.18 | (620) all_704_0 = all_676_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_630_3, all_704_0, zero_zero_int, % 238.22/37.18 | simplifying with (530), (547) gives: % 238.22/37.18 | (621) all_704_0 = all_630_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_447_0, all_710_1, zero_zero_int, % 238.22/37.18 | simplifying with (529), (555) gives: % 238.22/37.18 | (622) all_710_1 = all_447_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_656_1, all_728_2, zero_zero_int, % 238.22/37.18 | simplifying with (526), (540) gives: % 238.22/37.18 | (623) all_728_2 = all_656_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_687_3, all_755_3, zero_zero_int, % 238.22/37.18 | simplifying with (523), (532) gives: % 238.22/37.18 | (624) all_755_3 = all_687_3 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_634_1, all_755_3, zero_zero_int, % 238.22/37.18 | simplifying with (523), (545) gives: % 238.22/37.18 | (625) all_755_3 = all_634_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_764_2, all_769_3, zero_zero_int, % 238.22/37.18 | simplifying with (520), (522) gives: % 238.22/37.18 | (626) all_769_3 = all_764_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_749_2, all_769_3, zero_zero_int, % 238.22/37.18 | simplifying with (520), (525) gives: % 238.22/37.18 | (627) all_769_3 = all_749_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_698_2, all_772_2, zero_zero_int, % 238.22/37.18 | simplifying with (519), (531) gives: % 238.22/37.18 | (628) all_772_2 = all_698_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_674_2, all_772_2, zero_zero_int, % 238.22/37.18 | simplifying with (519), (535) gives: % 238.22/37.18 | (629) all_772_2 = all_674_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_658_1, all_784_2, zero_zero_int, % 238.22/37.18 | simplifying with (517), (539) gives: % 238.22/37.18 | (630) all_784_2 = all_658_1 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_443_0, all_784_2, zero_zero_int, % 238.22/37.18 | simplifying with (517), (557) gives: % 238.22/37.18 | (631) all_784_2 = all_443_0 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_644_2, all_841_2, zero_zero_int, % 238.22/37.18 | simplifying with (516), (543) gives: % 238.22/37.18 | (632) all_841_2 = all_644_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_639_2, all_841_2, zero_zero_int, % 238.22/37.18 | simplifying with (516), (544) gives: % 238.22/37.18 | (633) all_841_2 = all_639_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_775_2, all_844_4, zero_zero_int, % 238.22/37.18 | simplifying with (515), (518) gives: % 238.22/37.18 | (634) all_844_4 = all_775_2 % 238.22/37.18 | % 238.22/37.18 | GROUND_INST: instantiating (116) with all_710_1, all_868_2, zero_zero_int, % 238.22/37.18 | simplifying with (514), (529) gives: % 238.22/37.19 | (635) all_868_2 = all_710_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_844_4, all_895_2, zero_zero_int, % 238.22/37.19 | simplifying with (512), (515) gives: % 238.22/37.19 | (636) all_895_2 = all_844_4 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_868_2, all_937_2, zero_zero_int, % 238.22/37.19 | simplifying with (510), (514) gives: % 238.22/37.19 | (637) all_937_2 = all_868_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_772_2, all_940_2, zero_zero_int, % 238.22/37.19 | simplifying with (509), (519) gives: % 238.22/37.19 | (638) all_940_2 = all_772_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_767_2, all_940_2, zero_zero_int, % 238.22/37.19 | simplifying with (509), (521) gives: % 238.22/37.19 | (639) all_940_2 = all_767_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_895_2, all_943_2, zero_zero_int, % 238.22/37.19 | simplifying with (508), (512) gives: % 238.22/37.19 | (640) all_943_2 = all_895_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_668_2, all_943_2, zero_zero_int, % 238.22/37.19 | simplifying with (508), (538) gives: % 238.22/37.19 | (641) all_943_2 = all_668_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_784_2, all_952_2, zero_zero_int, % 238.22/37.19 | simplifying with (507), (517) gives: % 238.22/37.19 | (642) all_952_2 = all_784_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_952_2, all_1018_2, zero_zero_int, % 238.22/37.19 | simplifying with (506), (507) gives: % 238.22/37.19 | (643) all_1018_2 = all_952_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_784_2, all_1036_2, zero_zero_int, % 238.22/37.19 | simplifying with (505), (517) gives: % 238.22/37.19 | (644) all_1036_2 = all_784_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1036_2, all_1102_3, zero_zero_int, % 238.22/37.19 | simplifying with (504), (505) gives: % 238.22/37.19 | (645) all_1102_3 = all_1036_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_937_2, all_1111_1, zero_zero_int, % 238.22/37.19 | simplifying with (502), (510) gives: % 238.22/37.19 | (646) all_1111_1 = all_937_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_772_2, all_1132_1, zero_zero_int, % 238.22/37.19 | simplifying with (500), (519) gives: % 238.22/37.19 | (647) all_1132_1 = all_772_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_764_2, all_1132_1, zero_zero_int, % 238.22/37.19 | simplifying with (500), (522) gives: % 238.22/37.19 | (648) all_1132_1 = all_764_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_713_1, all_1132_1, zero_zero_int, % 238.22/37.19 | simplifying with (500), (528) gives: % 238.22/37.19 | (649) all_1132_1 = all_713_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_775_2, all_1135_3, zero_zero_int, % 238.22/37.19 | simplifying with (499), (518) gives: % 238.22/37.19 | (650) all_1135_3 = all_775_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_764_2, all_1135_3, zero_zero_int, % 238.22/37.19 | simplifying with (499), (522) gives: % 238.22/37.19 | (651) all_1135_3 = all_764_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1135_3, all_1138_3, zero_zero_int, % 238.22/37.19 | simplifying with (498), (499) gives: % 238.22/37.19 | (652) all_1138_3 = all_1135_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1018_2, all_1144_3, zero_zero_int, % 238.22/37.19 | simplifying with (497), (506) gives: % 238.22/37.19 | (653) all_1144_3 = all_1018_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_841_2, all_1150_3, zero_zero_int, % 238.22/37.19 | simplifying with (496), (516) gives: % 238.22/37.19 | (654) all_1150_3 = all_841_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_728_2, all_1150_3, zero_zero_int, % 238.22/37.19 | simplifying with (496), (526) gives: % 238.22/37.19 | (655) all_1150_3 = all_728_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_651_1, all_1150_3, zero_zero_int, % 238.22/37.19 | simplifying with (496), (541) gives: % 238.22/37.19 | (656) all_1150_3 = all_651_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1105_1, all_1159_3, zero_zero_int, % 238.22/37.19 | simplifying with (495), (503) gives: % 238.22/37.19 | (657) all_1159_3 = all_1105_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1138_3, all_1171_3, zero_zero_int, % 238.22/37.19 | simplifying with (493), (498) gives: % 238.22/37.19 | (658) all_1171_3 = all_1138_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1111_1, all_1174_3, zero_zero_int, % 238.22/37.19 | simplifying with (492), (502) gives: % 238.22/37.19 | (659) all_1174_3 = all_1111_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_674_2, all_1186_3, zero_zero_int, % 238.22/37.19 | simplifying with (491), (535) gives: % 238.22/37.19 | (660) all_1186_3 = all_674_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_672_3, all_1186_3, zero_zero_int, % 238.22/37.19 | simplifying with (491), (536) gives: % 238.22/37.19 | (661) all_1186_3 = all_672_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1186_3, all_1204_2, zero_zero_int, % 238.22/37.19 | simplifying with (490), (491) gives: % 238.22/37.19 | (662) all_1204_2 = all_1186_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1123_1, all_1204_2, zero_zero_int, % 238.22/37.19 | simplifying with (490), (501) gives: % 238.22/37.19 | (663) all_1204_2 = all_1123_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1105_1, all_1204_2, zero_zero_int, % 238.22/37.19 | simplifying with (490), (503) gives: % 238.22/37.19 | (664) all_1204_2 = all_1105_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_728_2, all_1204_2, zero_zero_int, % 238.22/37.19 | simplifying with (490), (526) gives: % 238.22/37.19 | (665) all_1204_2 = all_728_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_670_2, all_1204_2, zero_zero_int, % 238.22/37.19 | simplifying with (490), (537) gives: % 238.22/37.19 | (666) all_1204_2 = all_670_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1159_3, all_1207_2, zero_zero_int, % 238.22/37.19 | simplifying with (489), (495) gives: % 238.22/37.19 | (667) all_1207_2 = all_1159_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_445_0, all_1207_2, zero_zero_int, % 238.22/37.19 | simplifying with (489), (556) gives: % 238.22/37.19 | (668) all_1207_2 = all_445_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1144_3, all_1210_0, zero_zero_int, % 238.22/37.19 | simplifying with (488), (497) gives: % 238.22/37.19 | (669) all_1210_0 = all_1144_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_441_0, all_1210_0, zero_zero_int, % 238.22/37.19 | simplifying with (488), (558) gives: % 238.22/37.19 | (670) all_1210_0 = all_441_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1174_3, all_1213_0, zero_zero_int, % 238.22/37.19 | simplifying with (487), (492) gives: % 238.22/37.19 | (671) all_1213_0 = all_1174_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_439_0, all_1213_0, zero_zero_int, % 238.22/37.19 | simplifying with (487), (559) gives: % 238.22/37.19 | (672) all_1213_0 = all_439_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1165_3, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (494) gives: % 238.22/37.19 | (673) all_1216_0 = all_1165_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_928_2, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (511) gives: % 238.22/37.19 | (674) all_1216_0 = all_928_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_676_3, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (534) gives: % 238.22/37.19 | (675) all_1216_0 = all_676_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_649_2, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (542) gives: % 238.22/37.19 | (676) all_1216_0 = all_649_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_632_1, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (546) gives: % 238.22/37.19 | (677) all_1216_0 = all_632_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_628_1, all_1216_0, zero_zero_int, % 238.22/37.19 | simplifying with (486), (548) gives: % 238.22/37.19 | (678) all_1216_0 = all_628_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1102_3, all_1221_0, zero_zero_int, % 238.22/37.19 | simplifying with (485), (504) gives: % 238.22/37.19 | (679) all_1221_0 = all_1102_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_449_0, all_1221_0, zero_zero_int, % 238.22/37.19 | simplifying with (485), (554) gives: % 238.22/37.19 | (680) all_1221_0 = all_449_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_889_2, all_1224_2, zero_zero_int, % 238.22/37.19 | simplifying with (484), (513) gives: % 238.22/37.19 | (681) all_1224_2 = all_889_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_728_2, all_1224_2, zero_zero_int, % 238.22/37.19 | simplifying with (484), (526) gives: % 238.22/37.19 | (682) all_1224_2 = all_728_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_716_0, all_1224_2, zero_zero_int, % 238.22/37.19 | simplifying with (484), (527) gives: % 238.22/37.19 | (683) all_1224_2 = all_716_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_1171_3, all_1227_2, zero_zero_int, % 238.22/37.19 | simplifying with (483), (493) gives: % 238.22/37.19 | (684) all_1227_2 = all_1171_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (116) with all_752_3, all_1227_2, zero_zero_int, % 238.22/37.19 | simplifying with (483), (524) gives: % 238.22/37.19 | (685) all_1227_2 = all_752_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (117) with all_500_0, all_580_1, zero_zero_int, % 238.22/37.19 | simplifying with (480), (481) gives: % 238.22/37.19 | (686) all_580_1 = all_500_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (117) with all_580_1, all_594_1, zero_zero_int, % 238.22/37.19 | simplifying with (479), (480) gives: % 238.22/37.19 | (687) all_594_1 = all_580_1 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (117) with zero_zero_int, all_594_1, zero_zero_int, % 238.22/37.19 | simplifying with (479), (482) gives: % 238.22/37.19 | (688) all_594_1 = zero_zero_int % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (118) with all_632_3, all_799_0, one_one_nat, % 238.22/37.19 | simplifying with (181), (314) gives: % 238.22/37.19 | (689) all_799_0 = all_632_3 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (118) with all_621_2, all_799_0, one_one_nat, % 238.22/37.19 | simplifying with (166), (314) gives: % 238.22/37.19 | (690) all_799_0 = all_621_2 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (118) with all_799_0, all_1183_0, one_one_nat, % 238.22/37.19 | simplifying with (314), (445) gives: % 238.22/37.19 | (691) all_1183_0 = all_799_0 % 238.22/37.19 | % 238.22/37.19 | GROUND_INST: instantiating (118) with all_634_3, all_1183_0, one_one_nat, % 238.22/37.19 | simplifying with (186), (445) gives: % 238.22/37.19 | (692) all_1183_0 = all_634_3 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (608), (609) imply: % 238.22/37.19 | (693) all_1162_0 = all_477_1 % 238.22/37.19 | % 238.22/37.19 | SIMP: (693) implies: % 238.22/37.19 | (694) all_1162_0 = all_477_1 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (581), (582) imply: % 238.22/37.19 | (695) all_805_0 = all_658_3 % 238.22/37.19 | % 238.22/37.19 | SIMP: (695) implies: % 238.22/37.19 | (696) all_805_0 = all_658_3 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (684), (685) imply: % 238.22/37.19 | (697) all_1171_3 = all_752_3 % 238.22/37.19 | % 238.22/37.19 | SIMP: (697) implies: % 238.22/37.19 | (698) all_1171_3 = all_752_3 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (681), (683) imply: % 238.22/37.19 | (699) all_889_2 = all_716_0 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (681), (682) imply: % 238.22/37.19 | (700) all_889_2 = all_728_2 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (679), (680) imply: % 238.22/37.19 | (701) all_1102_3 = all_449_0 % 238.22/37.19 | % 238.22/37.19 | SIMP: (701) implies: % 238.22/37.19 | (702) all_1102_3 = all_449_0 % 238.22/37.19 | % 238.22/37.19 | COMBINE_EQS: (673), (677) imply: % 238.22/37.19 | (703) all_1165_3 = all_632_1 % 238.22/37.19 | % 238.22/37.20 | COMBINE_EQS: (673), (678) imply: % 238.22/37.20 | (704) all_1165_3 = all_628_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (673), (675) imply: % 238.22/37.20 | (705) all_1165_3 = all_676_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (673), (676) imply: % 238.22/37.20 | (706) all_1165_3 = all_649_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (673), (674) imply: % 238.22/37.20 | (707) all_1165_3 = all_928_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (671), (672) imply: % 238.22/37.20 | (708) all_1174_3 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (708) implies: % 238.22/37.20 | (709) all_1174_3 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (669), (670) imply: % 238.22/37.20 | (710) all_1144_3 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (710) implies: % 238.22/37.20 | (711) all_1144_3 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (667), (668) imply: % 238.22/37.20 | (712) all_1159_3 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (712) implies: % 238.22/37.20 | (713) all_1159_3 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (663), (666) imply: % 238.22/37.20 | (714) all_1123_1 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (663), (664) imply: % 238.22/37.20 | (715) all_1123_1 = all_1105_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (662), (663) imply: % 238.22/37.20 | (716) all_1186_3 = all_1123_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (716) implies: % 238.22/37.20 | (717) all_1186_3 = all_1123_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (663), (665) imply: % 238.22/37.20 | (718) all_1123_1 = all_728_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (605), (607) imply: % 238.22/37.20 | (719) all_1072_1 = all_519_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (605), (606) imply: % 238.22/37.20 | (720) all_1072_1 = all_734_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (661), (717) imply: % 238.22/37.20 | (721) all_1123_1 = all_672_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (721) implies: % 238.22/37.20 | (722) all_1123_1 = all_672_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (660), (661) imply: % 238.22/37.20 | (723) all_674_2 = all_672_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (723) implies: % 238.22/37.20 | (724) all_674_2 = all_672_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (691), (692) imply: % 238.22/37.20 | (725) all_799_0 = all_634_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (725) implies: % 238.22/37.20 | (726) all_799_0 = all_634_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (659), (709) imply: % 238.22/37.20 | (727) all_1111_1 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (727) implies: % 238.22/37.20 | (728) all_1111_1 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (658), (698) imply: % 238.22/37.20 | (729) all_1138_3 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (729) implies: % 238.22/37.20 | (730) all_1138_3 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (703), (707) imply: % 238.22/37.20 | (731) all_928_2 = all_632_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (706), (707) imply: % 238.22/37.20 | (732) all_928_2 = all_649_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (705), (707) imply: % 238.22/37.20 | (733) all_928_2 = all_676_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (704), (707) imply: % 238.22/37.20 | (734) all_928_2 = all_628_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (604), (694) imply: % 238.22/37.20 | (735) all_1099_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (735) implies: % 238.22/37.20 | (736) all_1099_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (657), (713) imply: % 238.22/37.20 | (737) all_1105_1 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (737) implies: % 238.22/37.20 | (738) all_1105_1 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (655), (656) imply: % 238.22/37.20 | (739) all_728_2 = all_651_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (739) implies: % 238.22/37.20 | (740) all_728_2 = all_651_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (654), (656) imply: % 238.22/37.20 | (741) all_841_2 = all_651_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (741) implies: % 238.22/37.20 | (742) all_841_2 = all_651_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (653), (711) imply: % 238.22/37.20 | (743) all_1018_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (743) implies: % 238.22/37.20 | (744) all_1018_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (652), (730) imply: % 238.22/37.20 | (745) all_1135_3 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (745) implies: % 238.22/37.20 | (746) all_1135_3 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (651), (746) imply: % 238.22/37.20 | (747) all_764_2 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (747) implies: % 238.22/37.20 | (748) all_764_2 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (650), (746) imply: % 238.22/37.20 | (749) all_775_2 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (749) implies: % 238.22/37.20 | (750) all_775_2 = all_752_3 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (647), (649) imply: % 238.22/37.20 | (751) all_772_2 = all_713_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (751) implies: % 238.22/37.20 | (752) all_772_2 = all_713_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (648), (649) imply: % 238.22/37.20 | (753) all_764_2 = all_713_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (753) implies: % 238.22/37.20 | (754) all_764_2 = all_713_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (714), (718) imply: % 238.22/37.20 | (755) all_728_2 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (755) implies: % 238.22/37.20 | (756) all_728_2 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (714), (715) imply: % 238.22/37.20 | (757) all_1105_1 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (757) implies: % 238.22/37.20 | (758) all_1105_1 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (714), (722) imply: % 238.22/37.20 | (759) all_672_3 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (759) implies: % 238.22/37.20 | (760) all_672_3 = all_670_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (646), (728) imply: % 238.22/37.20 | (761) all_937_2 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (761) implies: % 238.22/37.20 | (762) all_937_2 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (738), (758) imply: % 238.22/37.20 | (763) all_670_2 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (763) implies: % 238.22/37.20 | (764) all_670_2 = all_445_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (645), (702) imply: % 238.22/37.20 | (765) all_1036_2 = all_449_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (765) implies: % 238.22/37.20 | (766) all_1036_2 = all_449_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (603), (736) imply: % 238.22/37.20 | (767) all_1081_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (767) implies: % 238.22/37.20 | (768) all_1081_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (602), (768) imply: % 238.22/37.20 | (769) all_1078_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (769) implies: % 238.22/37.20 | (770) all_1078_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (601), (770) imply: % 238.22/37.20 | (771) all_1072_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (771) implies: % 238.22/37.20 | (772) all_1072_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (600), (772) imply: % 238.22/37.20 | (773) all_1066_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (773) implies: % 238.22/37.20 | (774) all_1066_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (719), (720) imply: % 238.22/37.20 | (775) all_734_0 = all_519_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (775) implies: % 238.22/37.20 | (776) all_734_0 = all_519_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (599), (774) imply: % 238.22/37.20 | (777) all_1054_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (777) implies: % 238.22/37.20 | (778) all_1054_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (598), (778) imply: % 238.22/37.20 | (779) all_1051_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (779) implies: % 238.22/37.20 | (780) all_1051_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (597), (780) imply: % 238.22/37.20 | (781) all_1036_3 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (781) implies: % 238.22/37.20 | (782) all_1036_3 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (644), (766) imply: % 238.22/37.20 | (783) all_784_2 = all_449_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (783) implies: % 238.22/37.20 | (784) all_784_2 = all_449_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (596), (782) imply: % 238.22/37.20 | (785) all_961_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (785) implies: % 238.22/37.20 | (786) all_961_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (643), (744) imply: % 238.22/37.20 | (787) all_952_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (787) implies: % 238.22/37.20 | (788) all_952_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (595), (786) imply: % 238.22/37.20 | (789) all_946_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (789) implies: % 238.22/37.20 | (790) all_946_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (642), (788) imply: % 238.22/37.20 | (791) all_784_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (791) implies: % 238.22/37.20 | (792) all_784_2 = all_441_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (594), (790) imply: % 238.22/37.20 | (793) all_931_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (793) implies: % 238.22/37.20 | (794) all_931_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (640), (641) imply: % 238.22/37.20 | (795) all_895_2 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (795) implies: % 238.22/37.20 | (796) all_895_2 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (638), (639) imply: % 238.22/37.20 | (797) all_772_2 = all_767_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (797) implies: % 238.22/37.20 | (798) all_772_2 = all_767_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (637), (762) imply: % 238.22/37.20 | (799) all_868_2 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (799) implies: % 238.22/37.20 | (800) all_868_2 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (593), (794) imply: % 238.22/37.20 | (801) all_907_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (801) implies: % 238.22/37.20 | (802) all_907_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (732), (733) imply: % 238.22/37.20 | (803) all_676_3 = all_649_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (803) implies: % 238.22/37.20 | (804) all_676_3 = all_649_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (732), (734) imply: % 238.22/37.20 | (805) all_649_2 = all_628_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (731), (732) imply: % 238.22/37.20 | (806) all_649_2 = all_632_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (592), (802) imply: % 238.22/37.20 | (807) all_901_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (807) implies: % 238.22/37.20 | (808) all_901_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (591), (808) imply: % 238.22/37.20 | (809) all_856_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (809) implies: % 238.22/37.20 | (810) all_856_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (636), (796) imply: % 238.22/37.20 | (811) all_844_4 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (811) implies: % 238.22/37.20 | (812) all_844_4 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (699), (700) imply: % 238.22/37.20 | (813) all_728_2 = all_716_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (813) implies: % 238.22/37.20 | (814) all_728_2 = all_716_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (635), (800) imply: % 238.22/37.20 | (815) all_710_1 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | SIMP: (815) implies: % 238.22/37.20 | (816) all_710_1 = all_439_0 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (590), (810) imply: % 238.22/37.20 | (817) all_835_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (817) implies: % 238.22/37.20 | (818) all_835_0 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (634), (812) imply: % 238.22/37.20 | (819) all_775_2 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (819) implies: % 238.22/37.20 | (820) all_775_2 = all_668_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (632), (633) imply: % 238.22/37.20 | (821) all_644_2 = all_639_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (632), (742) imply: % 238.22/37.20 | (822) all_651_1 = all_644_2 % 238.22/37.20 | % 238.22/37.20 | SIMP: (822) implies: % 238.22/37.20 | (823) all_651_1 = all_644_2 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (589), (818) imply: % 238.22/37.20 | (824) all_778_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | SIMP: (824) implies: % 238.22/37.20 | (825) all_778_1 = all_477_1 % 238.22/37.20 | % 238.22/37.20 | COMBINE_EQS: (580), (696) imply: % 238.22/37.20 | (826) all_778_0 = all_658_3 % 238.22/37.20 | % 238.22/37.20 | SIMP: (826) implies: % 238.22/37.20 | (827) all_778_0 = all_658_3 % 238.22/37.20 | % 238.22/37.21 | COMBINE_EQS: (690), (726) imply: % 238.22/37.21 | (828) all_634_3 = all_621_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (689), (726) imply: % 238.22/37.21 | (829) all_634_3 = all_632_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (630), (784) imply: % 238.22/37.21 | (830) all_658_1 = all_449_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (830) implies: % 238.22/37.21 | (831) all_658_1 = all_449_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (631), (784) imply: % 238.22/37.21 | (832) all_449_0 = all_443_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (784), (792) imply: % 238.22/37.21 | (833) all_449_0 = all_441_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (579), (827) imply: % 238.22/37.21 | (834) all_767_6 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (834) implies: % 238.22/37.21 | (835) all_767_6 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (588), (825) imply: % 238.22/37.21 | (836) all_707_1 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (836) implies: % 238.22/37.21 | (837) all_707_1 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (750), (820) imply: % 238.22/37.21 | (838) all_752_3 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (838) implies: % 238.22/37.21 | (839) all_752_3 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (628), (798) imply: % 238.22/37.21 | (840) all_767_2 = all_698_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (629), (798) imply: % 238.22/37.21 | (841) all_767_2 = all_674_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (752), (798) imply: % 238.22/37.21 | (842) all_767_2 = all_713_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (626), (627) imply: % 238.22/37.21 | (843) all_764_2 = all_749_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (843) implies: % 238.22/37.21 | (844) all_764_2 = all_749_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (840), (842) imply: % 238.22/37.21 | (845) all_713_1 = all_698_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (845) implies: % 238.22/37.21 | (846) all_713_1 = all_698_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (840), (841) imply: % 238.22/37.21 | (847) all_698_2 = all_674_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (568), (569) imply: % 238.22/37.21 | (848) all_685_2 = all_681_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (578), (835) imply: % 238.22/37.21 | (849) all_710_2 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (849) implies: % 238.22/37.21 | (850) all_710_2 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (754), (844) imply: % 238.22/37.21 | (851) all_749_2 = all_713_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (748), (844) imply: % 238.22/37.21 | (852) all_752_3 = all_749_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (852) implies: % 238.22/37.21 | (853) all_752_3 = all_749_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (624), (625) imply: % 238.22/37.21 | (854) all_687_3 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (854) implies: % 238.22/37.21 | (855) all_687_3 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (839), (853) imply: % 238.22/37.21 | (856) all_749_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (856) implies: % 238.22/37.21 | (857) all_749_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (851), (857) imply: % 238.22/37.21 | (858) all_713_1 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (858) implies: % 238.22/37.21 | (859) all_713_1 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (587), (776) imply: % 238.22/37.21 | (860) all_548_2 = all_519_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (860) implies: % 238.22/37.21 | (861) all_548_2 = all_519_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (623), (814) imply: % 238.22/37.21 | (862) all_716_0 = all_656_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (756), (814) imply: % 238.22/37.21 | (863) all_716_0 = all_670_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (740), (814) imply: % 238.22/37.21 | (864) all_716_0 = all_651_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (862), (864) imply: % 238.22/37.21 | (865) all_656_1 = all_651_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (862), (863) imply: % 238.22/37.21 | (866) all_670_2 = all_656_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (866) implies: % 238.22/37.21 | (867) all_670_2 = all_656_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (846), (859) imply: % 238.22/37.21 | (868) all_698_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (868) implies: % 238.22/37.21 | (869) all_698_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (622), (816) imply: % 238.22/37.21 | (870) all_447_0 = all_439_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (870) implies: % 238.22/37.21 | (871) all_447_0 = all_439_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (577), (850) imply: % 238.22/37.21 | (872) all_692_0 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (872) implies: % 238.22/37.21 | (873) all_692_0 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (586), (837) imply: % 238.22/37.21 | (874) all_685_4 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (874) implies: % 238.22/37.21 | (875) all_685_4 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (620), (621) imply: % 238.22/37.21 | (876) all_676_3 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (876) implies: % 238.22/37.21 | (877) all_676_3 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (847), (869) imply: % 238.22/37.21 | (878) all_674_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (878) implies: % 238.22/37.21 | (879) all_674_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (576), (873) imply: % 238.22/37.21 | (880) all_685_3 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (880) implies: % 238.22/37.21 | (881) all_685_3 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (619), (855) imply: % 238.22/37.21 | (882) all_683_3 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (882) implies: % 238.22/37.21 | (883) all_683_3 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (575), (881) imply: % 238.22/37.21 | (884) all_681_3 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (884) implies: % 238.22/37.21 | (885) all_681_3 = all_658_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (585), (875) imply: % 238.22/37.21 | (886) all_623_3 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (886) implies: % 238.22/37.21 | (887) all_623_3 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (617), (883) imply: % 238.22/37.21 | (888) all_639_2 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (888) implies: % 238.22/37.21 | (889) all_639_2 = all_634_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (618), (883) imply: % 238.22/37.21 | (890) all_634_1 = all_632_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (573), (885) imply: % 238.22/37.21 | (891) all_658_3 = all_641_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (572), (885) imply: % 238.22/37.21 | (892) all_658_3 = all_651_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (574), (885) imply: % 238.22/37.21 | (893) all_658_3 = all_623_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (804), (877) imply: % 238.22/37.21 | (894) all_649_2 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (894) implies: % 238.22/37.21 | (895) all_649_2 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (724), (879) imply: % 238.22/37.21 | (896) all_672_3 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (896) implies: % 238.22/37.21 | (897) all_672_3 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (760), (897) imply: % 238.22/37.21 | (898) all_670_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (898) implies: % 238.22/37.21 | (899) all_670_2 = all_668_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (867), (899) imply: % 238.22/37.21 | (900) all_668_2 = all_656_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (764), (899) imply: % 238.22/37.21 | (901) all_668_2 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (900), (901) imply: % 238.22/37.21 | (902) all_656_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (902) implies: % 238.22/37.21 | (903) all_656_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (615), (616) imply: % 238.22/37.21 | (904) all_453_0 = all_451_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (904) implies: % 238.22/37.21 | (905) all_453_0 = all_451_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (616), (831) imply: % 238.22/37.21 | (906) all_451_0 = all_449_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (891), (893) imply: % 238.22/37.21 | (907) all_641_0 = all_623_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (907) implies: % 238.22/37.21 | (908) all_641_0 = all_623_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (892), (893) imply: % 238.22/37.21 | (909) all_651_3 = all_623_2 % 238.22/37.21 | % 238.22/37.21 | SIMP: (909) implies: % 238.22/37.21 | (910) all_651_3 = all_623_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (865), (903) imply: % 238.22/37.21 | (911) all_651_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (911) implies: % 238.22/37.21 | (912) all_651_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (823), (912) imply: % 238.22/37.21 | (913) all_644_2 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (913) implies: % 238.22/37.21 | (914) all_644_2 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (571), (910) imply: % 238.22/37.21 | (915) all_623_2 = all_563_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (915) implies: % 238.22/37.21 | (916) all_623_2 = all_563_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (806), (895) imply: % 238.22/37.21 | (917) all_632_1 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | SIMP: (917) implies: % 238.22/37.21 | (918) all_632_1 = all_630_3 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (805), (895) imply: % 238.22/37.21 | (919) all_630_3 = all_628_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (821), (914) imply: % 238.22/37.21 | (920) all_639_2 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (920) implies: % 238.22/37.21 | (921) all_639_2 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (570), (908) imply: % 238.22/37.21 | (922) all_623_2 = all_612_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (922) implies: % 238.22/37.21 | (923) all_623_2 = all_612_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (889), (921) imply: % 238.22/37.21 | (924) all_634_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (924) implies: % 238.22/37.21 | (925) all_634_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (890), (925) imply: % 238.22/37.21 | (926) all_632_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (926) implies: % 238.22/37.21 | (927) all_632_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (828), (829) imply: % 238.22/37.21 | (928) all_632_3 = all_621_2 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (918), (927) imply: % 238.22/37.21 | (929) all_630_3 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (929) implies: % 238.22/37.21 | (930) all_630_3 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (919), (930) imply: % 238.22/37.21 | (931) all_628_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (931) implies: % 238.22/37.21 | (932) all_628_1 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (614), (932) imply: % 238.22/37.21 | (933) all_459_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (933) implies: % 238.22/37.21 | (934) all_459_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (916), (923) imply: % 238.22/37.21 | (935) all_612_0 = all_563_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (935) implies: % 238.22/37.21 | (936) all_612_0 = all_563_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (584), (887) imply: % 238.22/37.21 | (937) all_552_2 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (937) implies: % 238.22/37.21 | (938) all_552_2 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (687), (688) imply: % 238.22/37.21 | (939) all_580_1 = zero_zero_int % 238.22/37.21 | % 238.22/37.21 | SIMP: (939) implies: % 238.22/37.21 | (940) all_580_1 = zero_zero_int % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (686), (940) imply: % 238.22/37.21 | (941) all_500_0 = zero_zero_int % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (583), (938) imply: % 238.22/37.21 | (942) all_548_2 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (942) implies: % 238.22/37.21 | (943) all_548_2 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (861), (943) imply: % 238.22/37.21 | (944) all_519_1 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | SIMP: (944) implies: % 238.22/37.21 | (945) all_519_1 = all_477_1 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (613), (934) imply: % 238.22/37.21 | (946) all_457_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (946) implies: % 238.22/37.21 | (947) all_457_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (612), (947) imply: % 238.22/37.21 | (948) all_455_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (948) implies: % 238.22/37.21 | (949) all_455_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (611), (949) imply: % 238.22/37.21 | (950) all_453_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (950) implies: % 238.22/37.21 | (951) all_453_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (905), (951) imply: % 238.22/37.21 | (952) all_451_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (952) implies: % 238.22/37.21 | (953) all_451_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (906), (953) imply: % 238.22/37.21 | (954) all_449_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | SIMP: (954) implies: % 238.22/37.21 | (955) all_449_0 = all_445_0 % 238.22/37.21 | % 238.22/37.21 | COMBINE_EQS: (832), (955) imply: % 238.22/37.21 | (956) all_445_0 = all_443_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (833), (955) imply: % 238.22/37.22 | (957) all_445_0 = all_441_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (610), (871) imply: % 238.22/37.22 | (958) all_443_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | SIMP: (958) implies: % 238.22/37.22 | (959) all_443_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (956), (957) imply: % 238.22/37.22 | (960) all_443_0 = all_441_0 % 238.22/37.22 | % 238.22/37.22 | SIMP: (960) implies: % 238.22/37.22 | (961) all_443_0 = all_441_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (959), (961) imply: % 238.22/37.22 | (962) all_441_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (957), (962) imply: % 238.22/37.22 | (963) all_445_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (955), (963) imply: % 238.22/37.22 | (964) all_449_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (953), (963) imply: % 238.22/37.22 | (965) all_451_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (932), (963) imply: % 238.22/37.22 | (966) all_628_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (930), (963) imply: % 238.22/37.22 | (967) all_630_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (927), (963) imply: % 238.22/37.22 | (968) all_632_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (925), (963) imply: % 238.22/37.22 | (969) all_634_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (921), (963) imply: % 238.22/37.22 | (970) all_639_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (914), (963) imply: % 238.22/37.22 | (971) all_644_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (895), (967) imply: % 238.22/37.22 | (972) all_649_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (912), (963) imply: % 238.22/37.22 | (973) all_651_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (903), (963) imply: % 238.22/37.22 | (974) all_656_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (893), (916) imply: % 238.22/37.22 | (975) all_658_3 = all_563_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (616), (965) imply: % 238.22/37.22 | (976) all_658_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (901), (963) imply: % 238.22/37.22 | (977) all_668_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (899), (977) imply: % 238.22/37.22 | (978) all_670_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (897), (977) imply: % 238.22/37.22 | (979) all_672_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (879), (977) imply: % 238.22/37.22 | (980) all_674_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (885), (975) imply: % 238.22/37.22 | (981) all_681_3 = all_563_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (883), (969) imply: % 238.22/37.22 | (982) all_683_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (881), (975) imply: % 238.22/37.22 | (983) all_685_3 = all_563_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (855), (969) imply: % 238.22/37.22 | (984) all_687_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (869), (977) imply: % 238.22/37.22 | (985) all_698_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (862), (974) imply: % 238.22/37.22 | (986) all_716_0 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (814), (986) imply: % 238.22/37.22 | (987) all_728_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (857), (977) imply: % 238.22/37.22 | (988) all_749_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (839), (977) imply: % 238.22/37.22 | (989) all_752_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (625), (969) imply: % 238.22/37.22 | (990) all_755_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (844), (988) imply: % 238.22/37.22 | (991) all_764_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (835), (975) imply: % 238.22/37.22 | (992) all_767_6 = all_563_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (840), (985) imply: % 238.22/37.22 | (993) all_767_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (627), (988) imply: % 238.22/37.22 | (994) all_769_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (798), (993) imply: % 238.22/37.22 | (995) all_772_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (820), (977) imply: % 238.22/37.22 | (996) all_775_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (784), (964) imply: % 238.22/37.22 | (997) all_784_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (632), (971) imply: % 238.22/37.22 | (998) all_841_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (812), (977) imply: % 238.22/37.22 | (999) all_844_4 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (699), (986) imply: % 238.22/37.22 | (1000) all_889_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (796), (977) imply: % 238.22/37.22 | (1001) all_895_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (732), (972) imply: % 238.22/37.22 | (1002) all_928_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (639), (993) imply: % 238.22/37.22 | (1003) all_940_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (641), (977) imply: % 238.22/37.22 | (1004) all_943_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (788), (962) imply: % 238.22/37.22 | (1005) all_952_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (744), (962) imply: % 238.22/37.22 | (1006) all_1018_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (766), (964) imply: % 238.22/37.22 | (1007) all_1036_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (702), (964) imply: % 238.22/37.22 | (1008) all_1102_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (714), (978) imply: % 238.22/37.22 | (1009) all_1123_1 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (746), (989) imply: % 238.22/37.22 | (1010) all_1135_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (730), (989) imply: % 238.22/37.22 | (1011) all_1138_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (711), (962) imply: % 238.22/37.22 | (1012) all_1144_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (656), (973) imply: % 238.22/37.22 | (1013) all_1150_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (713), (963) imply: % 238.22/37.22 | (1014) all_1159_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (707), (1002) imply: % 238.22/37.22 | (1015) all_1165_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (698), (989) imply: % 238.22/37.22 | (1016) all_1171_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (661), (979) imply: % 238.22/37.22 | (1017) all_1186_3 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (663), (1009) imply: % 238.22/37.22 | (1018) all_1204_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (668), (963) imply: % 238.22/37.22 | (1019) all_1207_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (681), (1000) imply: % 238.22/37.22 | (1020) all_1224_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | COMBINE_EQS: (685), (989) imply: % 238.22/37.22 | (1021) all_1227_2 = all_439_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (185), (828) imply: % 238.22/37.22 | (1022) hAPP_nat_nat(all_621_2, one_one_nat) = all_634_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (180), (928) imply: % 238.22/37.22 | (1023) hAPP_nat_nat(all_621_2, one_one_nat) = all_632_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (473), (1021) imply: % 238.22/37.22 | (1024) bit0(all_439_0) = all_1227_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (469), (1020) imply: % 238.22/37.22 | (1025) bit0(all_439_0) = all_1224_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (457), (1019) imply: % 238.22/37.22 | (1026) bit0(all_439_0) = all_1207_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (453), (1018) imply: % 238.22/37.22 | (1027) bit0(all_439_0) = all_1204_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (448), (1017) imply: % 238.22/37.22 | (1028) bit0(all_439_0) = all_1186_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (442), (709) imply: % 238.22/37.22 | (1029) bit0(all_439_0) = all_1174_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (438), (1016) imply: % 238.22/37.22 | (1030) bit0(all_439_0) = all_1171_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (434), (1015) imply: % 238.22/37.22 | (1031) bit0(all_439_0) = all_1165_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (428), (1014) imply: % 238.22/37.22 | (1032) bit0(all_439_0) = all_1159_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (424), (1013) imply: % 238.22/37.22 | (1033) bit0(all_439_0) = all_1150_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (420), (1012) imply: % 238.22/37.22 | (1034) bit0(all_439_0) = all_1144_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (416), (1011) imply: % 238.22/37.22 | (1035) bit0(all_439_0) = all_1138_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (412), (1010) imply: % 238.22/37.22 | (1036) bit0(all_439_0) = all_1135_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (400), (1008) imply: % 238.22/37.22 | (1037) bit0(all_439_0) = all_1102_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (381), (1007) imply: % 238.22/37.22 | (1038) bit0(all_439_0) = all_1036_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (376), (1006) imply: % 238.22/37.22 | (1039) bit0(all_439_0) = all_1018_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (370), (1005) imply: % 238.22/37.22 | (1040) bit0(all_439_0) = all_952_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (363), (1004) imply: % 238.22/37.22 | (1041) bit0(all_439_0) = all_943_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (359), (1003) imply: % 238.22/37.22 | (1042) bit0(all_439_0) = all_940_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (355), (762) imply: % 238.22/37.22 | (1043) bit0(all_439_0) = all_937_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (349), (1002) imply: % 238.22/37.22 | (1044) bit0(all_439_0) = all_928_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (341), (1001) imply: % 238.22/37.22 | (1045) bit0(all_439_0) = all_895_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (337), (1000) imply: % 238.22/37.22 | (1046) bit0(all_439_0) = all_889_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (332), (800) imply: % 238.22/37.22 | (1047) bit0(all_439_0) = all_868_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (325), (999) imply: % 238.22/37.22 | (1048) bit0(all_439_0) = all_844_3 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (321), (998) imply: % 238.22/37.22 | (1049) bit0(all_439_0) = all_841_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (311), (997) imply: % 238.22/37.22 | (1050) bit0(all_439_0) = all_784_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (304), (996) imply: % 238.22/37.22 | (1051) bit0(all_439_0) = all_775_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (300), (995) imply: % 238.22/37.22 | (1052) bit0(all_439_0) = all_772_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (296), (994) imply: % 238.22/37.22 | (1053) bit0(all_439_0) = all_769_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (293), (993) imply: % 238.22/37.22 | (1054) bit0(all_439_0) = all_767_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (284), (991) imply: % 238.22/37.22 | (1055) bit0(all_439_0) = all_764_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (280), (990) imply: % 238.22/37.22 | (1056) bit0(all_439_0) = all_755_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (277), (989) imply: % 238.22/37.22 | (1057) bit0(all_439_0) = all_752_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (274), (988) imply: % 238.22/37.22 | (1058) bit0(all_439_0) = all_749_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (268), (987) imply: % 238.22/37.22 | (1059) bit0(all_439_0) = all_728_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (253), (985) imply: % 238.22/37.22 | (1060) bit0(all_439_0) = all_698_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (247), (984) imply: % 238.22/37.22 | (1061) bit0(all_439_0) = all_687_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (235), (982) imply: % 238.22/37.22 | (1062) bit0(all_439_0) = all_683_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (226), (980) imply: % 238.22/37.22 | (1063) bit0(all_439_0) = all_674_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (222), (979) imply: % 238.22/37.22 | (1064) bit0(all_439_0) = all_672_2 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (218), (978) imply: % 238.22/37.22 | (1065) bit0(all_439_0) = all_670_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (214), (977) imply: % 238.22/37.22 | (1066) bit0(all_439_0) = all_668_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (210), (976) imply: % 238.22/37.22 | (1067) bit0(all_439_0) = all_658_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (206), (974) imply: % 238.22/37.22 | (1068) bit0(all_439_0) = all_656_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (203), (973) imply: % 238.22/37.22 | (1069) bit0(all_439_0) = all_651_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (199), (972) imply: % 238.22/37.22 | (1070) bit0(all_439_0) = all_649_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (195), (971) imply: % 238.22/37.22 | (1071) bit0(all_439_0) = all_644_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (189), (970) imply: % 238.22/37.22 | (1072) bit0(all_439_0) = all_639_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (183), (969) imply: % 238.22/37.22 | (1073) bit0(all_439_0) = all_634_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (178), (968) imply: % 238.22/37.22 | (1074) bit0(all_439_0) = all_632_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (171), (966) imply: % 238.22/37.22 | (1075) bit0(all_439_0) = all_628_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (287), (569), (992) imply: % 238.22/37.22 | (1076) hAPP_int_int(all_563_0, all_681_2) = all_767_4 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (241), (848), (983) imply: % 238.22/37.22 | (1077) hAPP_int_int(all_563_0, all_681_2) = all_685_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (231), (981) imply: % 238.22/37.22 | (1078) hAPP_int_int(all_563_0, all_681_2) = all_681_1 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (239), (875) imply: % 238.22/37.22 | (1079) hAPP_int_bool(all_477_1, all_685_1) = all_685_0 % 238.22/37.22 | % 238.22/37.22 | REDUCE: (148), (941) imply: % 238.22/37.22 | (1080) $i(zero_zero_int) % 238.22/37.22 | % 238.22/37.22 | GROUND_INST: instantiating (119) with all_685_1, all_767_4, all_681_2, % 238.22/37.22 | all_563_0, simplifying with (1076), (1077) gives: % 238.22/37.22 | (1081) all_767_4 = all_685_1 % 238.22/37.22 | % 238.22/37.22 | GROUND_INST: instantiating (119) with all_681_1, all_767_4, all_681_2, % 238.22/37.22 | all_563_0, simplifying with (1076), (1078) gives: % 238.22/37.22 | (1082) all_767_4 = all_681_1 % 238.22/37.22 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_632_0, all_644_1, all_439_0, % 238.22/37.23 | simplifying with (1071), (1074) gives: % 238.22/37.23 | (1083) all_644_1 = all_632_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_628_0, all_651_0, all_439_0, % 238.22/37.23 | simplifying with (1069), (1075) gives: % 238.22/37.23 | (1084) all_651_0 = all_628_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_651_0, all_656_0, all_439_0, % 238.22/37.23 | simplifying with (1068), (1069) gives: % 238.22/37.23 | (1085) all_656_0 = all_651_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_656_0, all_658_0, all_439_0, % 238.22/37.23 | simplifying with (1067), (1068) gives: % 238.22/37.23 | (1086) all_658_0 = all_656_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_670_1, all_672_2, all_439_0, % 238.22/37.23 | simplifying with (1064), (1065) gives: % 238.22/37.23 | (1087) all_672_2 = all_670_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_672_2, all_674_1, all_439_0, % 238.22/37.23 | simplifying with (1063), (1064) gives: % 238.22/37.23 | (1088) all_674_1 = all_672_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_674_1, all_683_2, all_439_0, % 238.22/37.23 | simplifying with (1062), (1063) gives: % 238.22/37.23 | (1089) all_683_2 = all_674_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_683_2, all_698_1, all_439_0, % 238.22/37.23 | simplifying with (1060), (1062) gives: % 238.22/37.23 | (1090) all_698_1 = all_683_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_749_1, all_764_1, all_439_0, % 238.22/37.23 | simplifying with (1055), (1058) gives: % 238.22/37.23 | (1091) all_764_1 = all_749_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_767_1, all_775_1, all_439_0, % 238.22/37.23 | simplifying with (1051), (1054) gives: % 238.22/37.23 | (1092) all_775_1 = all_767_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_844_3, all_868_1, all_439_0, % 238.22/37.23 | simplifying with (1047), (1048) gives: % 238.22/37.23 | (1093) all_868_1 = all_844_3 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_868_1, all_895_1, all_439_0, % 238.22/37.23 | simplifying with (1045), (1047) gives: % 238.22/37.23 | (1094) all_895_1 = all_868_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_772_1, all_937_1, all_439_0, % 238.22/37.23 | simplifying with (1043), (1052) gives: % 238.22/37.23 | (1095) all_937_1 = all_772_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_698_1, all_937_1, all_439_0, % 238.22/37.23 | simplifying with (1043), (1060) gives: % 238.22/37.23 | (1096) all_937_1 = all_698_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_764_1, all_940_1, all_439_0, % 238.22/37.23 | simplifying with (1042), (1055) gives: % 238.22/37.23 | (1097) all_940_1 = all_764_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_668_1, all_940_1, all_439_0, % 238.22/37.23 | simplifying with (1042), (1066) gives: % 238.22/37.23 | (1098) all_940_1 = all_668_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_767_1, all_943_1, all_439_0, % 238.22/37.23 | simplifying with (1041), (1054) gives: % 238.22/37.23 | (1099) all_943_1 = all_767_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_752_2, all_943_1, all_439_0, % 238.22/37.23 | simplifying with (1041), (1057) gives: % 238.22/37.23 | (1100) all_943_1 = all_752_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_651_0, all_943_1, all_439_0, % 238.22/37.23 | simplifying with (1041), (1069) gives: % 238.22/37.23 | (1101) all_943_1 = all_651_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_889_1, all_952_1, all_439_0, % 238.22/37.23 | simplifying with (1040), (1046) gives: % 238.22/37.23 | (1102) all_952_1 = all_889_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_687_2, all_952_1, all_439_0, % 238.22/37.23 | simplifying with (1040), (1061) gives: % 238.22/37.23 | (1103) all_952_1 = all_687_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_895_1, all_1018_1, all_439_0, % 238.22/37.23 | simplifying with (1039), (1045) gives: % 238.22/37.23 | (1104) all_1018_1 = all_895_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1018_1, all_1036_1, all_439_0, % 238.22/37.23 | simplifying with (1038), (1039) gives: % 238.22/37.23 | (1105) all_1036_1 = all_1018_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_764_1, all_1102_2, all_439_0, % 238.22/37.23 | simplifying with (1037), (1055) gives: % 238.22/37.23 | (1106) all_1102_2 = all_764_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_755_2, all_1102_2, all_439_0, % 238.22/37.23 | simplifying with (1037), (1056) gives: % 238.22/37.23 | (1107) all_1102_2 = all_755_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_728_1, all_1102_2, all_439_0, % 238.22/37.23 | simplifying with (1037), (1059) gives: % 238.22/37.23 | (1108) all_1102_2 = all_728_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_670_1, all_1102_2, all_439_0, % 238.22/37.23 | simplifying with (1037), (1065) gives: % 238.22/37.23 | (1109) all_1102_2 = all_670_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_658_0, all_1102_2, all_439_0, % 238.22/37.23 | simplifying with (1037), (1067) gives: % 238.22/37.23 | (1110) all_1102_2 = all_658_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_943_1, all_1135_2, all_439_0, % 238.22/37.23 | simplifying with (1036), (1041) gives: % 238.22/37.23 | (1111) all_1135_2 = all_943_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1036_1, all_1138_2, all_439_0, % 238.22/37.23 | simplifying with (1035), (1038) gives: % 238.22/37.23 | (1112) all_1138_2 = all_1036_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_775_1, all_1144_2, all_439_0, % 238.22/37.23 | simplifying with (1034), (1051) gives: % 238.22/37.23 | (1113) all_1144_2 = all_775_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_889_1, all_1150_2, all_439_0, % 238.22/37.23 | simplifying with (1033), (1046) gives: % 238.22/37.23 | (1114) all_1150_2 = all_889_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_755_2, all_1150_2, all_439_0, % 238.22/37.23 | simplifying with (1033), (1056) gives: % 238.22/37.23 | (1115) all_1150_2 = all_755_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1135_2, all_1159_2, all_439_0, % 238.22/37.23 | simplifying with (1032), (1036) gives: % 238.22/37.23 | (1116) all_1159_2 = all_1135_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_943_1, all_1165_2, all_439_0, % 238.22/37.23 | simplifying with (1031), (1041) gives: % 238.22/37.23 | (1117) all_1165_2 = all_943_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_644_1, all_1165_2, all_439_0, % 238.22/37.23 | simplifying with (1031), (1071) gives: % 238.22/37.23 | (1118) all_1165_2 = all_644_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_634_0, all_1165_2, all_439_0, % 238.22/37.23 | simplifying with (1031), (1073) gives: % 238.22/37.23 | (1119) all_1165_2 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1144_2, all_1171_2, all_439_0, % 238.22/37.23 | simplifying with (1030), (1034) gives: % 238.22/37.23 | (1120) all_1171_2 = all_1144_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_639_1, all_1171_2, all_439_0, % 238.22/37.23 | simplifying with (1030), (1072) gives: % 238.22/37.23 | (1121) all_1171_2 = all_639_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_937_1, all_1174_2, all_439_0, % 238.22/37.23 | simplifying with (1029), (1043) gives: % 238.22/37.23 | (1122) all_1174_2 = all_937_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_844_3, all_1174_2, all_439_0, % 238.22/37.23 | simplifying with (1029), (1048) gives: % 238.22/37.23 | (1123) all_1174_2 = all_844_3 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_784_1, all_1174_2, all_439_0, % 238.22/37.23 | simplifying with (1029), (1050) gives: % 238.22/37.23 | (1124) all_1174_2 = all_784_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1150_2, all_1186_2, all_439_0, % 238.22/37.23 | simplifying with (1028), (1033) gives: % 238.22/37.23 | (1125) all_1186_2 = all_1150_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_769_2, all_1186_2, all_439_0, % 238.22/37.23 | simplifying with (1028), (1053) gives: % 238.22/37.23 | (1126) all_1186_2 = all_769_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1138_2, all_1204_1, all_439_0, % 238.22/37.23 | simplifying with (1027), (1035) gives: % 238.22/37.23 | (1127) all_1204_1 = all_1138_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_937_1, all_1207_1, all_439_0, % 238.22/37.23 | simplifying with (1026), (1043) gives: % 238.22/37.23 | (1128) all_1207_1 = all_937_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_928_1, all_1207_1, all_439_0, % 238.22/37.23 | simplifying with (1026), (1044) gives: % 238.22/37.23 | (1129) all_1207_1 = all_928_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1204_1, all_1224_1, all_439_0, % 238.22/37.23 | simplifying with (1025), (1027) gives: % 238.22/37.23 | (1130) all_1224_1 = all_1204_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_649_1, all_1224_1, all_439_0, % 238.22/37.23 | simplifying with (1025), (1070) gives: % 238.22/37.23 | (1131) all_1224_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_1159_2, all_1227_1, all_439_0, % 238.22/37.23 | simplifying with (1024), (1032) gives: % 238.22/37.23 | (1132) all_1227_1 = all_1159_2 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (115) with all_841_1, all_1227_1, all_439_0, % 238.22/37.23 | simplifying with (1024), (1049) gives: % 238.22/37.23 | (1133) all_1227_1 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (122) with all_621_1, all_634_2, one_one_nat, % 238.22/37.23 | all_621_2, simplifying with (165), (1022) gives: % 238.22/37.23 | (1134) all_634_2 = all_621_1 % 238.22/37.23 | % 238.22/37.23 | GROUND_INST: instantiating (122) with all_632_2, all_634_2, one_one_nat, % 238.22/37.23 | all_621_2, simplifying with (1022), (1023) gives: % 238.22/37.23 | (1135) all_634_2 = all_632_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1132), (1133) imply: % 238.22/37.23 | (1136) all_1159_2 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1136) implies: % 238.22/37.23 | (1137) all_1159_2 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1130), (1131) imply: % 238.22/37.23 | (1138) all_1204_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1138) implies: % 238.22/37.23 | (1139) all_1204_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1128), (1129) imply: % 238.22/37.23 | (1140) all_937_1 = all_928_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1140) implies: % 238.22/37.23 | (1141) all_937_1 = all_928_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1127), (1139) imply: % 238.22/37.23 | (1142) all_1138_2 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1142) implies: % 238.22/37.23 | (1143) all_1138_2 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1125), (1126) imply: % 238.22/37.23 | (1144) all_1150_2 = all_769_2 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1144) implies: % 238.22/37.23 | (1145) all_1150_2 = all_769_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1122), (1124) imply: % 238.22/37.23 | (1146) all_937_1 = all_784_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1146) implies: % 238.22/37.23 | (1147) all_937_1 = all_784_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1123), (1124) imply: % 238.22/37.23 | (1148) all_844_3 = all_784_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1148) implies: % 238.22/37.23 | (1149) all_844_3 = all_784_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1120), (1121) imply: % 238.22/37.23 | (1150) all_1144_2 = all_639_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1150) implies: % 238.22/37.23 | (1151) all_1144_2 = all_639_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1118), (1119) imply: % 238.22/37.23 | (1152) all_644_1 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1152) implies: % 238.22/37.23 | (1153) all_644_1 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1117), (1119) imply: % 238.22/37.23 | (1154) all_943_1 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1154) implies: % 238.22/37.23 | (1155) all_943_1 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1116), (1137) imply: % 238.22/37.23 | (1156) all_1135_2 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1156) implies: % 238.22/37.23 | (1157) all_1135_2 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1115), (1145) imply: % 238.22/37.23 | (1158) all_769_2 = all_755_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1114), (1145) imply: % 238.22/37.23 | (1159) all_889_1 = all_769_2 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1159) implies: % 238.22/37.23 | (1160) all_889_1 = all_769_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1113), (1151) imply: % 238.22/37.23 | (1161) all_775_1 = all_639_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1161) implies: % 238.22/37.23 | (1162) all_775_1 = all_639_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1112), (1143) imply: % 238.22/37.23 | (1163) all_1036_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1163) implies: % 238.22/37.23 | (1164) all_1036_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1111), (1157) imply: % 238.22/37.23 | (1165) all_943_1 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1165) implies: % 238.22/37.23 | (1166) all_943_1 = all_841_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1108), (1110) imply: % 238.22/37.23 | (1167) all_728_1 = all_658_0 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1107), (1108) imply: % 238.22/37.23 | (1168) all_755_2 = all_728_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1168) implies: % 238.22/37.23 | (1169) all_755_2 = all_728_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1106), (1108) imply: % 238.22/37.23 | (1170) all_764_1 = all_728_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1170) implies: % 238.22/37.23 | (1171) all_764_1 = all_728_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1108), (1109) imply: % 238.22/37.23 | (1172) all_728_1 = all_670_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1105), (1164) imply: % 238.22/37.23 | (1173) all_1018_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1173) implies: % 238.22/37.23 | (1174) all_1018_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1104), (1174) imply: % 238.22/37.23 | (1175) all_895_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1175) implies: % 238.22/37.23 | (1176) all_895_1 = all_649_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1102), (1103) imply: % 238.22/37.23 | (1177) all_889_1 = all_687_2 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1177) implies: % 238.22/37.23 | (1178) all_889_1 = all_687_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1099), (1166) imply: % 238.22/37.23 | (1179) all_841_1 = all_767_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1155), (1166) imply: % 238.22/37.23 | (1180) all_841_1 = all_634_0 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1101), (1166) imply: % 238.22/37.23 | (1181) all_841_1 = all_651_0 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1100), (1166) imply: % 238.22/37.23 | (1182) all_841_1 = all_752_2 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1097), (1098) imply: % 238.22/37.23 | (1183) all_764_1 = all_668_1 % 238.22/37.23 | % 238.22/37.23 | SIMP: (1183) implies: % 238.22/37.23 | (1184) all_764_1 = all_668_1 % 238.22/37.23 | % 238.22/37.23 | COMBINE_EQS: (1096), (1141) imply: % 238.51/37.23 | (1185) all_928_1 = all_698_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1141), (1147) imply: % 238.51/37.23 | (1186) all_928_1 = all_784_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1095), (1141) imply: % 238.51/37.23 | (1187) all_928_1 = all_772_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1186), (1187) imply: % 238.51/37.23 | (1188) all_784_1 = all_772_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1188) implies: % 238.51/37.23 | (1189) all_784_1 = all_772_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1185), (1187) imply: % 238.51/37.23 | (1190) all_772_1 = all_698_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1094), (1176) imply: % 238.51/37.23 | (1191) all_868_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1191) implies: % 238.51/37.23 | (1192) all_868_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1160), (1178) imply: % 238.51/37.23 | (1193) all_769_2 = all_687_2 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1193) implies: % 238.51/37.23 | (1194) all_769_2 = all_687_2 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1093), (1192) imply: % 238.51/37.23 | (1195) all_844_3 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1195) implies: % 238.51/37.23 | (1196) all_844_3 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1149), (1196) imply: % 238.51/37.23 | (1197) all_784_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1197) implies: % 238.51/37.23 | (1198) all_784_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1180), (1182) imply: % 238.51/37.23 | (1199) all_752_2 = all_634_0 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1179), (1182) imply: % 238.51/37.23 | (1200) all_767_1 = all_752_2 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1200) implies: % 238.51/37.23 | (1201) all_767_1 = all_752_2 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1181), (1182) imply: % 238.51/37.23 | (1202) all_752_2 = all_651_0 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1189), (1198) imply: % 238.51/37.23 | (1203) all_772_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1203) implies: % 238.51/37.23 | (1204) all_772_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1092), (1162) imply: % 238.51/37.23 | (1205) all_767_1 = all_639_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1205) implies: % 238.51/37.23 | (1206) all_767_1 = all_639_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1190), (1204) imply: % 238.51/37.23 | (1207) all_698_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1207) implies: % 238.51/37.23 | (1208) all_698_1 = all_649_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1158), (1194) imply: % 238.51/37.23 | (1209) all_755_2 = all_687_2 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1209) implies: % 238.51/37.23 | (1210) all_755_2 = all_687_2 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1201), (1206) imply: % 238.51/37.23 | (1211) all_752_2 = all_639_1 % 238.51/37.23 | % 238.51/37.23 | SIMP: (1211) implies: % 238.51/37.23 | (1212) all_752_2 = all_639_1 % 238.51/37.23 | % 238.51/37.23 | COMBINE_EQS: (1081), (1082) imply: % 238.51/37.24 | (1213) all_685_1 = all_681_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1213) implies: % 238.51/37.24 | (1214) all_685_1 = all_681_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1091), (1184) imply: % 238.51/37.24 | (1215) all_749_1 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1091), (1171) imply: % 238.51/37.24 | (1216) all_749_1 = all_728_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1169), (1210) imply: % 238.51/37.24 | (1217) all_728_1 = all_687_2 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1217) implies: % 238.51/37.24 | (1218) all_728_1 = all_687_2 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1199), (1212) imply: % 238.51/37.24 | (1219) all_639_1 = all_634_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1202), (1212) imply: % 238.51/37.24 | (1220) all_651_0 = all_639_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1220) implies: % 238.51/37.24 | (1221) all_651_0 = all_639_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1215), (1216) imply: % 238.51/37.24 | (1222) all_728_1 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1222) implies: % 238.51/37.24 | (1223) all_728_1 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1218), (1223) imply: % 238.51/37.24 | (1224) all_687_2 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1172), (1218) imply: % 238.51/37.24 | (1225) all_687_2 = all_670_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1167), (1218) imply: % 238.51/37.24 | (1226) all_687_2 = all_658_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1090), (1208) imply: % 238.51/37.24 | (1227) all_683_2 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1227) implies: % 238.51/37.24 | (1228) all_683_2 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1224), (1225) imply: % 238.51/37.24 | (1229) all_670_1 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1229) implies: % 238.51/37.24 | (1230) all_670_1 = all_668_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1224), (1226) imply: % 238.51/37.24 | (1231) all_668_1 = all_658_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1089), (1228) imply: % 238.51/37.24 | (1232) all_674_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1232) implies: % 238.51/37.24 | (1233) all_674_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1088), (1233) imply: % 238.51/37.24 | (1234) all_672_2 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1234) implies: % 238.51/37.24 | (1235) all_672_2 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1087), (1235) imply: % 238.51/37.24 | (1236) all_670_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1236) implies: % 238.51/37.24 | (1237) all_670_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1230), (1237) imply: % 238.51/37.24 | (1238) all_668_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1238) implies: % 238.51/37.24 | (1239) all_668_1 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1231), (1239) imply: % 238.51/37.24 | (1240) all_658_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1240) implies: % 238.51/37.24 | (1241) all_658_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1086), (1241) imply: % 238.51/37.24 | (1242) all_656_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1242) implies: % 238.51/37.24 | (1243) all_656_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1085), (1243) imply: % 238.51/37.24 | (1244) all_651_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1244) implies: % 238.51/37.24 | (1245) all_651_0 = all_649_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1084), (1245) imply: % 238.51/37.24 | (1246) all_649_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1221), (1245) imply: % 238.51/37.24 | (1247) all_649_1 = all_639_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1246), (1247) imply: % 238.51/37.24 | (1248) all_639_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1248) implies: % 238.51/37.24 | (1249) all_639_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1083), (1153) imply: % 238.51/37.24 | (1250) all_634_0 = all_632_0 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1250) implies: % 238.51/37.24 | (1251) all_634_0 = all_632_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1219), (1249) imply: % 238.51/37.24 | (1252) all_634_0 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1252) implies: % 238.51/37.24 | (1253) all_634_0 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1251), (1253) imply: % 238.51/37.24 | (1254) all_632_0 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1254) implies: % 238.51/37.24 | (1255) all_632_0 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1134), (1135) imply: % 238.51/37.24 | (1256) all_632_2 = all_621_1 % 238.51/37.24 | % 238.51/37.24 | SIMP: (1256) implies: % 238.51/37.24 | (1257) all_632_2 = all_621_1 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1083), (1255) imply: % 238.51/37.24 | (1258) all_644_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1239), (1246) imply: % 238.51/37.24 | (1259) all_668_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1237), (1246) imply: % 238.51/37.24 | (1260) all_670_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1235), (1246) imply: % 238.51/37.24 | (1261) all_672_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1233), (1246) imply: % 238.51/37.24 | (1262) all_674_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1224), (1259) imply: % 238.51/37.24 | (1263) all_687_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1208), (1246) imply: % 238.51/37.24 | (1264) all_698_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1218), (1263) imply: % 238.51/37.24 | (1265) all_728_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1215), (1259) imply: % 238.51/37.24 | (1266) all_749_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1212), (1249) imply: % 238.51/37.24 | (1267) all_752_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1091), (1266) imply: % 238.51/37.24 | (1268) all_764_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1206), (1249) imply: % 238.51/37.24 | (1269) all_767_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1194), (1263) imply: % 238.51/37.24 | (1270) all_769_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1204), (1246) imply: % 238.51/37.24 | (1271) all_772_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1162), (1249) imply: % 238.51/37.24 | (1272) all_775_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1198), (1246) imply: % 238.51/37.24 | (1273) all_784_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1182), (1267) imply: % 238.51/37.24 | (1274) all_841_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1196), (1246) imply: % 238.51/37.24 | (1275) all_844_3 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1192), (1246) imply: % 238.51/37.24 | (1276) all_868_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1176), (1246) imply: % 238.51/37.24 | (1277) all_895_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1187), (1271) imply: % 238.51/37.24 | (1278) all_928_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1141), (1278) imply: % 238.51/37.24 | (1279) all_937_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1098), (1259) imply: % 238.51/37.24 | (1280) all_940_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1166), (1274) imply: % 238.51/37.24 | (1281) all_943_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1103), (1263) imply: % 238.51/37.24 | (1282) all_952_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1174), (1246) imply: % 238.51/37.24 | (1283) all_1018_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1164), (1246) imply: % 238.51/37.24 | (1284) all_1036_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1108), (1265) imply: % 238.51/37.24 | (1285) all_1102_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1157), (1274) imply: % 238.51/37.24 | (1286) all_1135_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1143), (1246) imply: % 238.51/37.24 | (1287) all_1138_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1151), (1249) imply: % 238.51/37.24 | (1288) all_1144_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1145), (1270) imply: % 238.51/37.24 | (1289) all_1150_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1137), (1274) imply: % 238.51/37.24 | (1290) all_1159_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1119), (1253) imply: % 238.51/37.24 | (1291) all_1165_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1121), (1249) imply: % 238.51/37.24 | (1292) all_1171_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1124), (1273) imply: % 238.51/37.24 | (1293) all_1174_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1126), (1270) imply: % 238.51/37.24 | (1294) all_1186_2 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1139), (1246) imply: % 238.51/37.24 | (1295) all_1204_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1129), (1278) imply: % 238.51/37.24 | (1296) all_1207_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1131), (1246) imply: % 238.51/37.24 | (1297) all_1224_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | COMBINE_EQS: (1133), (1274) imply: % 238.51/37.24 | (1298) all_1227_1 = all_628_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (472), (1298) imply: % 238.51/37.24 | (1299) number_number_of_nat(all_628_0) = all_1227_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (468), (1297) imply: % 238.51/37.24 | (1300) number_number_of_nat(all_628_0) = all_1224_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (456), (1296) imply: % 238.51/37.24 | (1301) number_number_of_nat(all_628_0) = all_1207_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (452), (1295) imply: % 238.51/37.24 | (1302) number_number_of_nat(all_628_0) = all_1204_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (447), (1294) imply: % 238.51/37.24 | (1303) number_number_of_nat(all_628_0) = all_1186_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (441), (1293) imply: % 238.51/37.24 | (1304) number_number_of_nat(all_628_0) = all_1174_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (437), (1292) imply: % 238.51/37.24 | (1305) number_number_of_nat(all_628_0) = all_1171_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (433), (1291) imply: % 238.51/37.24 | (1306) number_number_of_nat(all_628_0) = all_1165_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (427), (1290) imply: % 238.51/37.24 | (1307) number_number_of_nat(all_628_0) = all_1159_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (423), (1289) imply: % 238.51/37.24 | (1308) number_number_of_nat(all_628_0) = all_1150_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (419), (1288) imply: % 238.51/37.24 | (1309) number_number_of_nat(all_628_0) = all_1144_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (415), (1287) imply: % 238.51/37.24 | (1310) number_number_of_nat(all_628_0) = all_1138_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (411), (1286) imply: % 238.51/37.24 | (1311) number_number_of_nat(all_628_0) = all_1135_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (399), (1285) imply: % 238.51/37.24 | (1312) number_number_of_nat(all_628_0) = all_1102_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (380), (1284) imply: % 238.51/37.24 | (1313) number_number_of_nat(all_628_0) = all_1036_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (375), (1283) imply: % 238.51/37.24 | (1314) number_number_of_nat(all_628_0) = all_1018_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (369), (1282) imply: % 238.51/37.24 | (1315) number_number_of_nat(all_628_0) = all_952_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (362), (1281) imply: % 238.51/37.24 | (1316) number_number_of_nat(all_628_0) = all_943_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (358), (1280) imply: % 238.51/37.24 | (1317) number_number_of_nat(all_628_0) = all_940_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (354), (1279) imply: % 238.51/37.24 | (1318) number_number_of_nat(all_628_0) = all_937_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (348), (1278) imply: % 238.51/37.24 | (1319) number_number_of_nat(all_628_0) = all_928_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (340), (1277) imply: % 238.51/37.24 | (1320) number_number_of_nat(all_628_0) = all_895_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (331), (1276) imply: % 238.51/37.24 | (1321) number_number_of_nat(all_628_0) = all_868_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (324), (1275) imply: % 238.51/37.24 | (1322) number_number_of_nat(all_628_0) = all_844_2 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (320), (1274) imply: % 238.51/37.24 | (1323) number_number_of_nat(all_628_0) = all_841_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (310), (1273) imply: % 238.51/37.24 | (1324) number_number_of_nat(all_628_0) = all_784_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (303), (1272) imply: % 238.51/37.24 | (1325) number_number_of_nat(all_628_0) = all_775_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (299), (1271) imply: % 238.51/37.24 | (1326) number_number_of_nat(all_628_0) = all_772_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (292), (1269) imply: % 238.51/37.24 | (1327) number_number_of_nat(all_628_0) = all_767_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (283), (1268) imply: % 238.51/37.24 | (1328) number_number_of_nat(all_628_0) = all_764_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (273), (1266) imply: % 238.51/37.24 | (1329) number_number_of_nat(all_628_0) = all_749_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (267), (1265) imply: % 238.51/37.24 | (1330) number_number_of_nat(all_628_0) = all_728_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (252), (1264) imply: % 238.51/37.24 | (1331) number_number_of_nat(all_628_0) = all_698_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (246), (1263) imply: % 238.51/37.24 | (1332) number_number_of_nat(all_628_0) = all_687_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (225), (1262) imply: % 238.51/37.24 | (1333) number_number_of_nat(all_628_0) = all_674_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (221), (1261) imply: % 238.51/37.24 | (1334) number_number_of_nat(all_628_0) = all_672_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (217), (1260) imply: % 238.51/37.24 | (1335) number_number_of_nat(all_628_0) = all_670_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (213), (1259) imply: % 238.51/37.24 | (1336) number_number_of_nat(all_628_0) = all_668_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (198), (1246) imply: % 238.51/37.24 | (1337) number_number_of_nat(all_628_0) = all_649_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (194), (1258) imply: % 238.51/37.24 | (1338) number_number_of_nat(all_628_0) = all_644_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (188), (1249) imply: % 238.51/37.24 | (1339) number_number_of_nat(all_628_0) = all_639_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (177), (1255), (1257) imply: % 238.51/37.24 | (1340) number_number_of_nat(all_628_0) = all_621_1 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (291), (1082) imply: % 238.51/37.24 | (1341) power_power_int(all_681_1) = all_767_3 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (1079), (1214) imply: % 238.51/37.24 | (1342) hAPP_int_bool(all_477_1, all_681_1) = all_685_0 % 238.51/37.24 | % 238.51/37.24 | REDUCE: (238), (1214) imply: % 238.51/37.24 | (1343) $i(all_681_1) % 238.51/37.24 | % 238.51/37.24 | REDUCE: (176), (1255) imply: % 238.51/37.24 | (1344) $i(all_628_0) % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_672_0, all_698_0, all_628_0, % 238.51/37.24 | simplifying with (1331), (1334) gives: % 238.51/37.24 | (1345) all_698_0 = all_672_0 % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_668_0, all_698_0, all_628_0, % 238.51/37.24 | simplifying with (1331), (1336) gives: % 238.51/37.24 | (1346) all_698_0 = all_668_0 % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_687_1, all_728_0, all_628_0, % 238.51/37.24 | simplifying with (1330), (1332) gives: % 238.51/37.24 | (1347) all_728_0 = all_687_1 % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_728_0, all_749_0, all_628_0, % 238.51/37.24 | simplifying with (1329), (1330) gives: % 238.51/37.24 | (1348) all_749_0 = all_728_0 % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_687_1, all_764_0, all_628_0, % 238.51/37.24 | simplifying with (1328), (1332) gives: % 238.51/37.24 | (1349) all_764_0 = all_687_1 % 238.51/37.24 | % 238.51/37.24 | GROUND_INST: instantiating (114) with all_672_0, all_764_0, all_628_0, % 238.51/37.24 | simplifying with (1328), (1334) gives: % 238.51/37.25 | (1350) all_764_0 = all_672_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_749_0, all_767_0, all_628_0, % 238.51/37.25 | simplifying with (1327), (1329) gives: % 238.51/37.25 | (1351) all_767_0 = all_749_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_775_0, all_841_0, all_628_0, % 238.51/37.25 | simplifying with (1323), (1325) gives: % 238.51/37.25 | (1352) all_841_0 = all_775_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_698_0, all_844_2, all_628_0, % 238.51/37.25 | simplifying with (1322), (1331) gives: % 238.51/37.25 | (1353) all_844_2 = all_698_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_668_0, all_928_0, all_628_0, % 238.51/37.25 | simplifying with (1319), (1336) gives: % 238.51/37.25 | (1354) all_928_0 = all_668_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_895_0, all_937_0, all_628_0, % 238.51/37.25 | simplifying with (1318), (1320) gives: % 238.51/37.25 | (1355) all_937_0 = all_895_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_621_1, all_940_0, all_628_0, % 238.51/37.25 | simplifying with (1317), (1340) gives: % 238.51/37.25 | (1356) all_940_0 = all_621_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_775_0, all_943_0, all_628_0, % 238.51/37.25 | simplifying with (1316), (1325) gives: % 238.51/37.25 | (1357) all_943_0 = all_775_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_772_0, all_943_0, all_628_0, % 238.51/37.25 | simplifying with (1316), (1326) gives: % 238.51/37.25 | (1358) all_943_0 = all_772_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_767_0, all_943_0, all_628_0, % 238.51/37.25 | simplifying with (1316), (1327) gives: % 238.51/37.25 | (1359) all_943_0 = all_767_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_940_0, all_952_0, all_628_0, % 238.51/37.25 | simplifying with (1315), (1317) gives: % 238.51/37.25 | (1360) all_952_0 = all_940_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_928_0, all_952_0, all_628_0, % 238.51/37.25 | simplifying with (1315), (1319) gives: % 238.51/37.25 | (1361) all_952_0 = all_928_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_644_0, all_952_0, all_628_0, % 238.51/37.25 | simplifying with (1315), (1338) gives: % 238.51/37.25 | (1362) all_952_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_844_2, all_1036_0, all_628_0, % 238.51/37.25 | simplifying with (1313), (1322) gives: % 238.51/37.25 | (1363) all_1036_0 = all_844_2 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_895_0, all_1102_1, all_628_0, % 238.51/37.25 | simplifying with (1312), (1320) gives: % 238.51/37.25 | (1364) all_1102_1 = all_895_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_868_0, all_1102_1, all_628_0, % 238.51/37.25 | simplifying with (1312), (1321) gives: % 238.51/37.25 | (1365) all_1102_1 = all_868_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_841_0, all_1102_1, all_628_0, % 238.51/37.25 | simplifying with (1312), (1323) gives: % 238.51/37.25 | (1366) all_1102_1 = all_841_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_928_0, all_1135_1, all_628_0, % 238.51/37.25 | simplifying with (1311), (1319) gives: % 238.51/37.25 | (1367) all_1135_1 = all_928_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1135_1, all_1138_1, all_628_0, % 238.51/37.25 | simplifying with (1310), (1311) gives: % 238.51/37.25 | (1368) all_1138_1 = all_1135_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1036_0, all_1144_1, all_628_0, % 238.51/37.25 | simplifying with (1309), (1313) gives: % 238.51/37.25 | (1369) all_1144_1 = all_1036_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_764_0, all_1150_1, all_628_0, % 238.51/37.25 | simplifying with (1308), (1328) gives: % 238.51/37.25 | (1370) all_1150_1 = all_764_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_674_0, all_1150_1, all_628_0, % 238.51/37.25 | simplifying with (1308), (1333) gives: % 238.51/37.25 | (1371) all_1150_1 = all_674_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_943_0, all_1159_1, all_628_0, % 238.51/37.25 | simplifying with (1307), (1316) gives: % 238.51/37.25 | (1372) all_1159_1 = all_943_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_784_0, all_1159_1, all_628_0, % 238.51/37.25 | simplifying with (1307), (1324) gives: % 238.51/37.25 | (1373) all_1159_1 = all_784_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1144_1, all_1171_1, all_628_0, % 238.51/37.25 | simplifying with (1305), (1309) gives: % 238.51/37.25 | (1374) all_1171_1 = all_1144_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_670_0, all_1171_1, all_628_0, % 238.51/37.25 | simplifying with (1305), (1335) gives: % 238.51/37.25 | (1375) all_1171_1 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1138_1, all_1174_1, all_628_0, % 238.51/37.25 | simplifying with (1304), (1310) gives: % 238.51/37.25 | (1376) all_1174_1 = all_1138_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1018_0, all_1186_1, all_628_0, % 238.51/37.25 | simplifying with (1303), (1314) gives: % 238.51/37.25 | (1377) all_1186_1 = all_1018_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_937_0, all_1186_1, all_628_0, % 238.51/37.25 | simplifying with (1303), (1318) gives: % 238.51/37.25 | (1378) all_1186_1 = all_937_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_639_0, all_1186_1, all_628_0, % 238.51/37.25 | simplifying with (1303), (1339) gives: % 238.51/37.25 | (1379) all_1186_1 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1174_1, all_1204_0, all_628_0, % 238.51/37.25 | simplifying with (1302), (1304) gives: % 238.51/37.25 | (1380) all_1204_0 = all_1174_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1207_0, all_1224_0, all_628_0, % 238.51/37.25 | simplifying with (1300), (1301) gives: % 238.51/37.25 | (1381) all_1224_0 = all_1207_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1204_0, all_1224_0, all_628_0, % 238.51/37.25 | simplifying with (1300), (1302) gives: % 238.51/37.25 | (1382) all_1224_0 = all_1204_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_649_0, all_1224_0, all_628_0, % 238.51/37.25 | simplifying with (1300), (1337) gives: % 238.51/37.25 | (1383) all_1224_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1186_1, all_1227_0, all_628_0, % 238.51/37.25 | simplifying with (1299), (1303) gives: % 238.51/37.25 | (1384) all_1227_0 = all_1186_1 % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (114) with all_1165_1, all_1227_0, all_628_0, % 238.51/37.25 | simplifying with (1299), (1306) gives: % 238.51/37.25 | (1385) all_1227_0 = all_1165_1 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1384), (1385) imply: % 238.51/37.25 | (1386) all_1186_1 = all_1165_1 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1386) implies: % 238.51/37.25 | (1387) all_1186_1 = all_1165_1 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1381), (1383) imply: % 238.51/37.25 | (1388) all_1207_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1381), (1382) imply: % 238.51/37.25 | (1389) all_1207_0 = all_1204_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1388), (1389) imply: % 238.51/37.25 | (1390) all_1204_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1390) implies: % 238.51/37.25 | (1391) all_1204_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1380), (1391) imply: % 238.51/37.25 | (1392) all_1174_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1392) implies: % 238.51/37.25 | (1393) all_1174_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1378), (1387) imply: % 238.51/37.25 | (1394) all_1165_1 = all_937_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1377), (1387) imply: % 238.51/37.25 | (1395) all_1165_1 = all_1018_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1379), (1387) imply: % 238.51/37.25 | (1396) all_1165_1 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1376), (1393) imply: % 238.51/37.25 | (1397) all_1138_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1397) implies: % 238.51/37.25 | (1398) all_1138_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1374), (1375) imply: % 238.51/37.25 | (1399) all_1144_1 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1399) implies: % 238.51/37.25 | (1400) all_1144_1 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1394), (1395) imply: % 238.51/37.25 | (1401) all_1018_0 = all_937_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1395), (1396) imply: % 238.51/37.25 | (1402) all_1018_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1372), (1373) imply: % 238.51/37.25 | (1403) all_943_0 = all_784_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1403) implies: % 238.51/37.25 | (1404) all_943_0 = all_784_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1370), (1371) imply: % 238.51/37.25 | (1405) all_764_0 = all_674_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1405) implies: % 238.51/37.25 | (1406) all_764_0 = all_674_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1369), (1400) imply: % 238.51/37.25 | (1407) all_1036_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1407) implies: % 238.51/37.25 | (1408) all_1036_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1368), (1398) imply: % 238.51/37.25 | (1409) all_1135_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1409) implies: % 238.51/37.25 | (1410) all_1135_1 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1367), (1410) imply: % 238.51/37.25 | (1411) all_928_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1411) implies: % 238.51/37.25 | (1412) all_928_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1364), (1365) imply: % 238.51/37.25 | (1413) all_895_0 = all_868_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1413) implies: % 238.51/37.25 | (1414) all_895_0 = all_868_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1365), (1366) imply: % 238.51/37.25 | (1415) all_868_0 = all_841_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1363), (1408) imply: % 238.51/37.25 | (1416) all_844_2 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1416) implies: % 238.51/37.25 | (1417) all_844_2 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1401), (1402) imply: % 238.51/37.25 | (1418) all_937_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1418) implies: % 238.51/37.25 | (1419) all_937_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1360), (1362) imply: % 238.51/37.25 | (1420) all_940_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1420) implies: % 238.51/37.25 | (1421) all_940_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1361), (1362) imply: % 238.51/37.25 | (1422) all_928_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1422) implies: % 238.51/37.25 | (1423) all_928_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1359), (1404) imply: % 238.51/37.25 | (1424) all_784_0 = all_767_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1358), (1404) imply: % 238.51/37.25 | (1425) all_784_0 = all_772_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1357), (1404) imply: % 238.51/37.25 | (1426) all_784_0 = all_775_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1356), (1421) imply: % 238.51/37.25 | (1427) all_644_0 = all_621_1 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1427) implies: % 238.51/37.25 | (1428) all_644_0 = all_621_1 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1355), (1419) imply: % 238.51/37.25 | (1429) all_895_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1429) implies: % 238.51/37.25 | (1430) all_895_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1354), (1412) imply: % 238.51/37.25 | (1431) all_668_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1431) implies: % 238.51/37.25 | (1432) all_668_0 = all_649_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1412), (1423) imply: % 238.51/37.25 | (1433) all_649_0 = all_644_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1414), (1430) imply: % 238.51/37.25 | (1434) all_868_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1434) implies: % 238.51/37.25 | (1435) all_868_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1415), (1435) imply: % 238.51/37.25 | (1436) all_841_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1436) implies: % 238.51/37.25 | (1437) all_841_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1353), (1417) imply: % 238.51/37.25 | (1438) all_698_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1438) implies: % 238.51/37.25 | (1439) all_698_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1352), (1437) imply: % 238.51/37.25 | (1440) all_775_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1440) implies: % 238.51/37.25 | (1441) all_775_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1425), (1426) imply: % 238.51/37.25 | (1442) all_775_0 = all_772_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1442) implies: % 238.51/37.25 | (1443) all_775_0 = all_772_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1424), (1425) imply: % 238.51/37.25 | (1444) all_772_0 = all_767_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1441), (1443) imply: % 238.51/37.25 | (1445) all_772_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1445) implies: % 238.51/37.25 | (1446) all_772_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1444), (1446) imply: % 238.51/37.25 | (1447) all_767_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1447) implies: % 238.51/37.25 | (1448) all_767_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1351), (1448) imply: % 238.51/37.25 | (1449) all_749_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1449) implies: % 238.51/37.25 | (1450) all_749_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1350), (1406) imply: % 238.51/37.25 | (1451) all_674_0 = all_672_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1349), (1406) imply: % 238.51/37.25 | (1452) all_687_1 = all_674_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1452) implies: % 238.51/37.25 | (1453) all_687_1 = all_674_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1348), (1450) imply: % 238.51/37.25 | (1454) all_728_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1454) implies: % 238.51/37.25 | (1455) all_728_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1347), (1455) imply: % 238.51/37.25 | (1456) all_687_1 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1456) implies: % 238.51/37.25 | (1457) all_687_1 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1346), (1439) imply: % 238.51/37.25 | (1458) all_670_0 = all_668_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1345), (1439) imply: % 238.51/37.25 | (1459) all_672_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1459) implies: % 238.51/37.25 | (1460) all_672_0 = all_670_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1453), (1457) imply: % 238.51/37.25 | (1461) all_674_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1461) implies: % 238.51/37.25 | (1462) all_674_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1451), (1462) imply: % 238.51/37.25 | (1463) all_672_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1463) implies: % 238.51/37.25 | (1464) all_672_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1460), (1464) imply: % 238.51/37.25 | (1465) all_670_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1465) implies: % 238.51/37.25 | (1466) all_670_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1458), (1466) imply: % 238.51/37.25 | (1467) all_668_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1467) implies: % 238.51/37.25 | (1468) all_668_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1432), (1468) imply: % 238.51/37.25 | (1469) all_649_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1469) implies: % 238.51/37.25 | (1470) all_649_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1433), (1470) imply: % 238.51/37.25 | (1471) all_644_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | SIMP: (1471) implies: % 238.51/37.25 | (1472) all_644_0 = all_639_0 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1428), (1472) imply: % 238.51/37.25 | (1473) all_639_0 = all_621_1 % 238.51/37.25 | % 238.51/37.25 | COMBINE_EQS: (1448), (1473) imply: % 238.51/37.25 | (1474) all_767_0 = all_621_1 % 238.51/37.25 | % 238.51/37.25 | REDUCE: (289), (1474) imply: % 238.51/37.25 | (1475) hAPP_nat_int(all_767_3, all_621_1) = zero_zero_int % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (36) with n, all_681_2, simplifying with (110), % 238.51/37.25 | (232) gives: % 238.51/37.25 | (1476) number_number_of_int(all_681_2) = all_681_2 & $i(all_681_2) % 238.51/37.25 | % 238.51/37.25 | ALPHA: (1476) implies: % 238.51/37.25 | (1477) $i(all_681_2) % 238.51/37.25 | % 238.51/37.25 | GROUND_INST: instantiating (36) with one_one_nat, one_one_int, simplifying % 238.51/37.25 | with (61), (107) gives: % 238.51/37.25 | (1478) number_number_of_int(one_one_int) = one_one_int & $i(one_one_int) % 238.51/37.25 | % 238.51/37.25 | ALPHA: (1478) implies: % 238.51/37.25 | (1479) $i(one_one_int) % 238.51/37.25 | % 238.51/37.26 | GROUND_INST: instantiating (367) with zero_zero_int, all_681_2, one_one_int, % 238.51/37.26 | all_477_1, all_563_0, all_681_1, all_685_0, simplifying with % 238.51/37.26 | (146), (157), (1078), (1080), (1342), (1477), (1479) gives: % 238.51/37.26 | (1480) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 238.51/37.26 | any] : ? [v5: any] : (hAPP_i1948725293t_bool(ord_less_eq_int, % 238.51/37.26 | zero_zero_int) = v2 & hBOOL(v3) = v4 & hBOOL(v0) = v1 & % 238.51/37.26 | hBOOL(all_685_0) = v5 & hAPP_int_bool(v2, all_681_2) = v3 & % 238.51/37.26 | hAPP_int_bool(all_946_0, one_one_int) = v0 & $i(v3) & $i(v2) & % 238.51/37.26 | $i(v0) & ( ~ (v4 = 0) | ~ (v1 = 0) | v5 = 0)) % 238.51/37.26 | % 238.51/37.26 | GROUND_INST: instantiating (335) with zero_zero_int, all_681_2, one_one_int, % 238.51/37.26 | all_477_1, all_563_0, all_681_1, all_685_0, simplifying with % 238.51/37.26 | (146), (157), (1078), (1080), (1342), (1477), (1479) gives: % 238.51/37.26 | (1481) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 238.51/37.26 | any] : (hBOOL(v2) = v3 & hBOOL(v0) = v1 & hBOOL(all_685_0) = v4 & % 238.51/37.26 | hAPP_int_bool(all_880_0, one_one_int) = v0 & % 238.51/37.26 | hAPP_int_bool(all_477_1, all_681_2) = v2 & $i(v2) & $i(v0) & ( ~ % 238.51/37.26 | (v3 = 0) | ~ (v1 = 0) | v4 = 0)) % 238.51/37.26 | % 238.51/37.26 | GROUND_INST: instantiating (329) with zero_zero_int, all_681_2, one_one_int, % 238.51/37.26 | all_477_1, all_563_0, all_681_1, all_685_0, simplifying with % 238.51/37.26 | (146), (157), (1078), (1080), (1342), (1477), (1479) gives: % 238.51/37.26 | (1482) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 238.51/37.26 | any] : (hBOOL(v2) = v3 & hBOOL(v0) = v1 & hBOOL(all_685_0) = v4 & % 238.51/37.26 | hAPP_int_bool(all_856_0, one_one_int) = v0 & % 238.51/37.26 | hAPP_int_bool(all_477_1, all_681_2) = v2 & $i(v2) & $i(v0) & ( ~ % 238.51/37.26 | (v3 = 0) | ~ (v1 = 0) | v4 = 0)) % 238.51/37.26 | % 238.51/37.26 | GROUND_INST: instantiating (70) with zero_zero_int, all_681_1, all_477_1, % 238.51/37.26 | all_685_0, simplifying with (146), (1080), (1342), (1343) gives: % 238.51/37.26 | (1483) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 238.51/37.26 | (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v1 & % 238.51/37.26 | hBOOL(v2) = v3 & hBOOL(all_685_0) = v0 & hAPP_int_bool(v1, % 238.51/37.26 | all_681_1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | (v3 = 0 & ~ % 238.51/37.26 | (all_681_1 = zero_zero_int)))) % 238.51/37.26 | % 238.51/37.26 | GROUND_INST: instantiating (33) with all_681_1, all_628_0, all_767_3, % 238.51/37.26 | all_621_1, simplifying with (1340), (1341), (1343), (1344), % 238.51/37.26 | (1475) gives: % 238.51/37.26 | (1484) all_681_1 = zero_zero_int & ~ (all_621_1 = zero_zero_nat) % 238.51/37.26 | % 238.51/37.26 | ALPHA: (1484) implies: % 238.51/37.26 | (1485) all_681_1 = zero_zero_int % 238.51/37.26 | % 238.51/37.26 | DELTA: instantiating (1483) with fresh symbols all_1520_0, all_1520_1, % 238.51/37.26 | all_1520_2, all_1520_3 gives: % 238.51/37.26 | (1486) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1520_2 % 238.51/37.26 | & hBOOL(all_1520_1) = all_1520_0 & hBOOL(all_685_0) = all_1520_3 & % 238.51/37.26 | hAPP_int_bool(all_1520_2, all_681_1) = all_1520_1 & $i(all_1520_1) & % 238.51/37.26 | $i(all_1520_2) & ( ~ (all_1520_3 = 0) | (all_1520_0 = 0 & ~ % 238.51/37.26 | (all_681_1 = zero_zero_int))) % 238.51/37.26 | % 238.51/37.26 | ALPHA: (1486) implies: % 238.51/37.26 | (1487) hBOOL(all_685_0) = all_1520_3 % 238.51/37.26 | (1488) ~ (all_1520_3 = 0) | (all_1520_0 = 0 & ~ (all_681_1 = % 238.51/37.26 | zero_zero_int)) % 238.51/37.26 | % 238.51/37.26 | DELTA: instantiating (1482) with fresh symbols all_1558_0, all_1558_1, % 238.51/37.26 | all_1558_2, all_1558_3, all_1558_4 gives: % 238.51/37.26 | (1489) hBOOL(all_1558_2) = all_1558_1 & hBOOL(all_1558_4) = all_1558_3 & % 238.51/37.26 | hBOOL(all_685_0) = all_1558_0 & hAPP_int_bool(all_856_0, % 238.51/37.26 | one_one_int) = all_1558_4 & hAPP_int_bool(all_477_1, all_681_2) = % 238.51/37.26 | all_1558_2 & $i(all_1558_2) & $i(all_1558_4) & ( ~ (all_1558_1 = 0) % 238.51/37.26 | | ~ (all_1558_3 = 0) | all_1558_0 = 0) % 238.51/37.26 | % 238.51/37.26 | ALPHA: (1489) implies: % 238.51/37.26 | (1490) hBOOL(all_685_0) = all_1558_0 % 238.51/37.26 | % 238.51/37.26 | DELTA: instantiating (1481) with fresh symbols all_1560_0, all_1560_1, % 238.51/37.26 | all_1560_2, all_1560_3, all_1560_4 gives: % 238.51/37.26 | (1491) hBOOL(all_1560_2) = all_1560_1 & hBOOL(all_1560_4) = all_1560_3 & % 238.51/37.26 | hBOOL(all_685_0) = all_1560_0 & hAPP_int_bool(all_880_0, % 238.51/37.26 | one_one_int) = all_1560_4 & hAPP_int_bool(all_477_1, all_681_2) = % 238.51/37.26 | all_1560_2 & $i(all_1560_2) & $i(all_1560_4) & ( ~ (all_1560_1 = 0) % 238.51/37.26 | | ~ (all_1560_3 = 0) | all_1560_0 = 0) % 238.51/37.26 | % 238.51/37.26 | ALPHA: (1491) implies: % 238.51/37.26 | (1492) hBOOL(all_685_0) = all_1560_0 % 238.51/37.26 | % 238.51/37.26 | DELTA: instantiating (1480) with fresh symbols all_1712_0, all_1712_1, % 238.51/37.26 | all_1712_2, all_1712_3, all_1712_4, all_1712_5 gives: % 238.51/37.26 | (1493) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1712_3 % 238.51/37.26 | & hBOOL(all_1712_2) = all_1712_1 & hBOOL(all_1712_5) = all_1712_4 & % 238.51/37.26 | hBOOL(all_685_0) = all_1712_0 & hAPP_int_bool(all_1712_3, all_681_2) % 238.51/37.26 | = all_1712_2 & hAPP_int_bool(all_946_0, one_one_int) = all_1712_5 & % 238.51/37.26 | $i(all_1712_2) & $i(all_1712_3) & $i(all_1712_5) & ( ~ (all_1712_1 = % 238.51/37.26 | 0) | ~ (all_1712_4 = 0) | all_1712_0 = 0) % 238.51/37.26 | % 238.51/37.26 | ALPHA: (1493) implies: % 238.51/37.26 | (1494) hBOOL(all_685_0) = all_1712_0 % 238.51/37.26 | % 238.51/37.26 | BETA: splitting (1488) gives: % 238.51/37.26 | % 238.51/37.26 | Case 1: % 238.51/37.26 | | % 238.51/37.26 | | (1495) ~ (all_1520_3 = 0) % 238.51/37.26 | | % 238.51/37.26 | | GROUND_INST: instantiating (112) with 0, all_1712_0, all_685_0, simplifying % 238.51/37.26 | | with (240), (1494) gives: % 238.51/37.26 | | (1496) all_1712_0 = 0 % 238.51/37.26 | | % 238.51/37.26 | | GROUND_INST: instantiating (112) with all_1560_0, all_1712_0, all_685_0, % 238.51/37.26 | | simplifying with (1492), (1494) gives: % 238.51/37.26 | | (1497) all_1712_0 = all_1560_0 % 238.51/37.26 | | % 238.51/37.26 | | GROUND_INST: instantiating (112) with all_1558_0, all_1712_0, all_685_0, % 238.51/37.26 | | simplifying with (1490), (1494) gives: % 238.51/37.26 | | (1498) all_1712_0 = all_1558_0 % 238.51/37.26 | | % 238.51/37.26 | | GROUND_INST: instantiating (112) with all_1520_3, all_1712_0, all_685_0, % 238.51/37.26 | | simplifying with (1487), (1494) gives: % 238.51/37.26 | | (1499) all_1712_0 = all_1520_3 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1496), (1497) imply: % 238.51/37.26 | | (1500) all_1560_0 = 0 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1497), (1499) imply: % 238.51/37.26 | | (1501) all_1560_0 = all_1520_3 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1497), (1498) imply: % 238.51/37.26 | | (1502) all_1560_0 = all_1558_0 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1501), (1502) imply: % 238.51/37.26 | | (1503) all_1558_0 = all_1520_3 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1500), (1502) imply: % 238.51/37.26 | | (1504) all_1558_0 = 0 % 238.51/37.26 | | % 238.51/37.26 | | COMBINE_EQS: (1503), (1504) imply: % 238.51/37.26 | | (1505) all_1520_3 = 0 % 238.51/37.26 | | % 238.51/37.26 | | SIMP: (1505) implies: % 238.51/37.26 | | (1506) all_1520_3 = 0 % 238.51/37.26 | | % 238.51/37.26 | | REDUCE: (1495), (1506) imply: % 238.51/37.26 | | (1507) $false % 238.51/37.26 | | % 238.51/37.26 | | CLOSE: (1507) is inconsistent. % 238.51/37.26 | | % 238.51/37.26 | Case 2: % 238.51/37.26 | | % 238.51/37.26 | | (1508) all_1520_0 = 0 & ~ (all_681_1 = zero_zero_int) % 238.51/37.26 | | % 238.51/37.26 | | ALPHA: (1508) implies: % 238.51/37.26 | | (1509) ~ (all_681_1 = zero_zero_int) % 238.51/37.26 | | % 238.51/37.26 | | REDUCE: (1485), (1509) imply: % 238.51/37.26 | | (1510) $false % 238.51/37.26 | | % 238.51/37.26 | | CLOSE: (1510) is inconsistent. % 238.51/37.26 | | % 238.51/37.26 | End of split % 238.51/37.26 | % 238.51/37.26 End of proof % 238.51/37.26 % SZS output end Proof for theBenchmark % 238.51/37.27 % 238.51/37.27 36673ms %------------------------------------------------------------------------------